Quantum Reports doi: 10.3390/quantum8030075

Authors: Angelo Plastino

The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article, we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom (REFF). From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.

Quantum Reports doi: 10.3390/quantum8030074

Authors: Nikita Semenin Ksenia Khabarova Nikolay Kolachevsky

High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer–Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges that influence the gate fidelity the most: “fast” noise at frequencies near the motional mode spectrum, and “slow” noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.

Quantum Reports doi: 10.3390/quantum8030073

Authors: Demerson N. Gonçalves Tharso D. Fernandes Andrias M. M. Cordeiro Pedro H. G. Lugao João T. Dias Fernando M. Araújo Moreira

The minimum accuracy heuristic provides a training-free way to evaluate quantum feature maps, but its original formulation assumes balanced datasets, requires an exhaustive Pauli-axis scan, and lacks a formal lower-bound interpretation. In this work, we generalize the metric to arbitrary binary datasets and prove that the resulting generalized minimum accuracy, denoted Rmin, is a certified lower bound on the optimal empirical accuracy R* achievable by linear classifiers in the same feature space. To improve scalability, we introduce Monte Carlo axis-selection strategies that estimate Rmin from random subsets of Pauli-feature axes and derive quantile-coverage guarantees for sampling high-accuracy directions. We validate the framework using exact statevector simulations of an n=6 qubit quantum feature map, corresponding to d=46=4096 Pauli axes, over 30 independent runs on five synthetic datasets. The proposed methods sample as few as 60 axes, produce lower-bound estimates and achieve speedups of approximately 27× to 68× compared with exhaustive evaluation. The results support generalized minimum accuracy as a scalable and theoretically grounded tool for pre-screening quantum feature maps in simulated quantum-kernel workflows.

Quantum Reports doi: 10.3390/quantum8030072

Authors: Georgios I. Alamanos

Understanding whether the mathematical structure of quantum mechanics is fundamental or emergent remains a central question in the foundations of physics. In particular, the special role played by time in quantum theory, appearing as an external evolution parameter rather than a dynamical observable, suggests that the formalism itself may arise from deeper structural considerations. In this work, we investigate the emergence of quantum mechanical formalism from classical wave dynamics by adopting a dimensional framework in which time is treated as a +1 evolution parameter relative to the dimensions through which physical phenomena (fields or disturbances of a field) propagate and interact. Within this perspective, different fields may evolve with respect to different effective dimensions, while remaining embedded in a common higher-dimensional space, allowing time to acquire a relational and context-dependent role. This means that in our proposed model, time is not a fixed dimension which is experienced the same way for every field or field interaction of any dimensionality. In that sense, time for one physical phenomenon can behave as space for a higher dimensional physical phenomenon, whose time is a different +1 dimension. The central objective of this paper is to determine how a higher-dimensional deterministic field can be consistently represented by a lower-dimensional description that lacks direct access to its full set of evolution parameters and evolves through a spatial (for the higher-dimensional field) dimension. To this end, we introduce a general projection framework in which a higher-dimensional field is mapped to a reduced field through an interaction-based recording process. Crucially, we do not assume the form of this mapping a priori. Instead, we impose the requirement that it preserve the maximum amount of physically accessible information. In particular, we demand the faithful encoding of phase relations, interference structure, and spectral composition, including the relative contributions of different Fourier modes and their superposition. We first demonstrate, within a purely classical 3 + 1-dimensional wave framework that these constraints severely restrict the admissible form of the reduced description and naturally lead to complex amplitudes, linear superposition, Hilbert space structure, and canonical operator relations. This analysis provides an intuitive and mathematically explicit route to quantum-like descriptions without assuming quantum postulates. We then generalize the construction to a 4 + 1-dimensional framework, introducing an additional evolution parameter and showing that under the same information-preserving constraints, the Schrödinger equation appears as an effective low-energy description of the reduced dynamics, while a relativistic dispersion relation emerges simultaneously through the encoding of the hidden evolution parameter as an invariant frequency scale. In this way, within the restricted single-field and free-dynamical sector considered here, quantum-compatible kinematical structures and relativistic dispersion arise from the same underlying requirement: the consistent and information-preserving representation of higher-dimensional wave propagation in a lower-dimensional observational framework. The present construction motivates a complex linear state space, an invariant quadratic norm, translation-generated canonical operator relations, norm-preserving evolution, and a Schrödinger-type low-energy equation, while composite-system structure, particle statistics or interacting multiparticle dynamics remain necessary subjects for future development. The results suggest that the formal structure of quantum mechanics need not be postulated a priori, but may instead be understood as the unique mathematical language required to encode the observable remnant of a higher-dimensional deterministic dynamics under strict constraints of symmetry, invariance, and information preservation.

Quantum Reports doi: 10.3390/quantum8030071

Authors: Mehmet Kilicarslan

We derive the reduced-spin von Neumann entropy generated by unitary Stern–Gerlach spin–position entanglement in a closed system. For any pure two-branch state with normalized spatial branches, the reduced-spin spectrum and entropy are determined entirely by the initial spin population p and the magnitude |γ| of the spatial branch overlap. This constitutes an exact, model-independent two-branch overlap law. For equal-width, unchirped Gaussian branches, |γ| = exp(−κ), where κ = Δx2/(8σx2) + σx2Δp2/(2ℏ2) is a quadratic phase-space distinguishability parameter that combines relative position and momentum displacements. The Gaussian entropy can therefore be written as Ss(κ,p), although this particular phase-space expression for κ does not generally apply to arbitrary wave-packet shapes. We derive the reduced density matrix and its spectrum, the equal-width Gaussian reduction, the constant-gradient form of κ(t), the weak-distinguishability onset and saturation limits, and an entropy response function. We also derive the overlap for freely spreading, chirped equal-width Gaussians and for unequal-width unchirped Gaussians, for which the fixed-width parameter κ is replaced by the corresponding Gaussian overlap coordinate. Different apparatus settings generally produce different entropy trajectories in time; at a fixed input population, these trajectories collapse only after reparametrization in terms of the appropriate overlap coordinate.

Quantum Reports doi: 10.3390/quantum8030070

Authors: Bin Li

The charged-lepton pole masses exhibit the well-known Koide relation, in which the square-root geometry reduces the three-mass pattern to a one-angle problem. This paper first gives a self-contained algebraic formulation of that geometry: the Koide condition is equivalent to equality between the democratic and orthogonal components of the charged-lepton root vector, and the resulting spectrum lies on a cone around the democratic direction. The geometric equivalence and the one-angle parameterization are exact. A reconstruction framework is then summarized to motivate a neutral-parent interpretation of the root space. In this framework, premetric equivalence gives equal structural weighting, the Indefinite Reconstruction Stability Principle motivates minimal saturation, and persistent charged readouts are associated with carrier-supported codimension-two holonomy structure. The remaining Koide cone angle is assigned by a phenomenological weak-closure selector constructed from the electron, proton, and neutron masses and the low-energy fine-structure constant. No continuous coefficient is optimized against the muon or tau mass, but the selector was formulated retrospectively rather than selected from a prespecified finite hypothesis class. The retained baseline selector gives a muon mass output of approximately 105.6565 MeV and a tau mass output of approximately 1776.94 MeV, with relative deviations of approximately 0.0017 percent below and 0.00061 percent above the adopted pole-mass values. Accordingly, the numerical agreement is reported descriptively and is not assigned a look-elsewhere-corrected statistical significance. The selector is an ansatz motivated by the reconstruction picture; its full form and coefficients are not yet derived from a complete premetric calculus or matched to a post-readout effective action. Therefore, the result is presented as reproducible pole mass phenomenology and as a concrete target for future formal reconstruction rather than as a derivation of running Standard Model Yukawa couplings.

Quantum Reports doi: 10.3390/quantum8030069

Authors: Ruwanga Konara Kasun De Zoysa Anuradha Mahasinghe Asanka Sayakkara Nalin Ranasinghe

Rapid progress in quantum computing threatens the long-term security of classical cryptographic primitives, and with them the integrity of contemporary blockchain systems that rely fundamentally on computational hardness assumptions. Hence, quantum-native blockchain architectures have emerged as a conceptual pathway toward information-theoretic disturbance detectability. Two influential approaches have emerged in the literature. The temporal GHZ-state blockchain provides disturbance-detectable tamper sensitivity through entanglement in time, whereas the weighted quantum-hypergraph blockchain achieves high encoding efficiency through phase-based quantum representations of classical information. However, each addresses only part of the problem. In this work, we introduce a hybrid quantum blockchain framework whose primary novelty is the integration of phase-encoded classical data representation with recursively generated temporal GHZ entanglement within a single blockchain architecture. Rather than proposing a new encoding scheme or a new temporal-entanglement construction, the framework combines both mechanisms found in the literature and introduces a corresponding verification procedure for validating phase-encoded temporally entangled blocks. This architecture preserves the physics-based measurement-disturbance detectability of temporal entanglement while enabling more efficient classical-to-quantum data encoding inspired by hypergraph-based phase weighting. The result is a conceptual blockchain model that simultaneously enhances tamper sensitivity and encoding efficiency, providing a coherent foundation for future research on secure and practical quantum-era ledger systems.

Quantum Reports doi: 10.3390/quantum8030068

Authors: Bharath G. Srivats

Three results. (1) We prove the tensor-level conformal identity dsBK2=4γ2(r) dsBures2 between the Bures metric and the Beltrami–Klein metric on the open qubit Bloch ball, where γ2(r)=1/(1−r2) is the squared Lorentz factor. (2) For the visibility coordinate V=2p−1 of a binary quantum measurement, the classical Bernoulli Fisher information takes the closed form I(V)=1/(1−V2)=γ2(V). (3) The conformal structure is special to qubits; for N≥3, the Bures metric on full-rank density matrices has a non-constant sectional curvature at the maximally mixed state and hence a non-vanishing Weyl tensor and no conformal equivalence to any constant-curvature hyperbolic model (Theorem 2). We outline an experimentally testable operational consequence where sequential non-collinear weak measurements on a qubit predict a Thomas–Wigner rotation with a closed-form purity dependence that deviates from the Pancharatnam baseline at intermediate visibility.

Quantum Reports doi: 10.3390/quantum8030067

Authors: Angelo Plastino

We address the problem of determining whether a given mixed quantum state corresponds to thermal equilibrium or to a zero-temperature statistical mixture. We show that geometric observables, in particular the quantum Fisher information, provide a direct diagnostic criterion. Thermal states satisfy fluctuation–response relations linking energy variance to parameter sensitivity, while generic mixed states do not. This establishes a geometric test of thermality that does not require prior knowledge of the Hamiltonian and connects requilibrium statistical mechanics with quantum information geometry.

Quantum Reports doi: 10.3390/quantum8030066

Authors: Venkatesan Narayanaswamy

The quantum measurement problem separates into operational questions: which observables are stable records, how outcome probabilities are represented, how conditional post-event states are updated, and how a detector event time is assigned. We give a compact architecture-conditional framework. In a finite-dimensional detector model, the detector-side relative-entropy flux is differentiated with the exact Fréchet derivative of the matrix logarithm. A noise-regularised timing distribution is defined and, under an explicitly assumed isolated non-degenerate maximum of the calibrated flux, Laplace asymptotics proves concentration at that maximum. Under stated fixed-point and detailed-balance hypotheses, the centre of the fixed-point algebra gives a canonical commutative record algebra. Outcome probabilities admit a POVM representation, and conditional updates use a completely positive (CP) instrument in its standard sense: CP maps whose traces give probabilities and whose normalised outputs give post-event states, summing to a trace-preserving map. Separately, an assumed modular-invariant inclusion of von Neumann algebras admits a state-preserving conditional expectation and CP retraction. A conditional quantum-error-correction lemma bounds accumulated record failure. These results do not derive unique outcomes from unitarity, construct a black-hole algebra inclusion, or resolve the black-hole information problem; they give a conditional framework, a worked illustration, and testable timing and record-stability criteria.

Quantum Reports doi: 10.3390/quantum8030065

Authors: Volodymyr Krasnoholovets

This paper re-examines quantum tunnelling—the penetration of a potential barrier by a subatomic particle—through the lens of classical wave dynamics. The author contends that applying the standard Schrödinger equation to this phenomenon lacks a solid physical foundation, whereas a classical wave description inherently necessitates a propagation medium. This requirement provides further evidence for a discrete, submicroscopic spatial structure: the tessellattice. By treating space as a physical substrate rather than an empty vacuum, this study identifies the source of intrinsic noise in quantum systems as inertons—mass perturbations generated by the internal dynamics of the tessellattice. While current quantum technologies rely on extreme cryogenic cooling to suppress noise, this paper argues that the abstract mathematical framework of standard quantum mechanics cannot fundamentally account for these vacuum-based fluctuations. By treating the tessellattice as a dynamic substrate, this work establishes a novel physical basis for understanding and mitigating qubit decoherence, offering a concrete, structural alternative to conventional cryogenic noise-reduction strategies.

Quantum Reports doi: 10.3390/quantum8030064

Authors: Daniel Santiago

Nucleic acids exhibit structured electromagnetic features shaped by classical electronegativity (EN) patterns. Mapping Pauling EN values across DNA and RNA reveals a largely invariant, high-EN phosphodiester backbone that provides a consistent electrostatic scaffold, while nucleobases introduce sequence-specific electron density shifts that generate tunable recognition fields. Together, these features create a dual-system framework in which a stable electrostatic background supports sequence-dependent informational cues. Within this environment, short-timescale vibronic interactions may arise from patterned vibrational and electronic behavior, producing modest “quantum overlay” effects compatible with known decoherence constraints. These structured, anisotropic electrostatic features may help explain differences in stability between DNA and RNA, the functional outcomes of nucleoside modifications such as N1-methylpseudouridine (m1Ψ), and the sensitivity of translational fidelity to small architectural perturbations. The framework yields experimentally testable predictions involving vibrational relaxation, dipole reorientation, and charge-transfer behavior, offering a classical-to-quantum interpretive bridge that may inform the design of next-generation therapeutic mRNAs.

Quantum Reports doi: 10.3390/quantum8030063

Authors: Andrei Tudor Patrascu

The central charge occupies a unique role in conformal field theory, simultaneously serving as a measure of degrees of freedom, as the determinant of Casimir energy through modular transformations, and as an obstruction to the naive extension of the Witt algebra. The Virasoro central extension itself is rigid: it fixes c as a label of a given conformal field theory. In this work, we propose that higher categorical coherence—the pentagon and hexagon constraints governing fusion and braiding data, one level above the cocycle responsible for the Virasoro extension—supplies an additional, physically controllable handle. We show that controlled deformations of this higher coherence (higher categorical coherence breakdown, HCCB), implemented consistently through anomaly inflow, shift the effective central charge read out by anomaly-sensitive observables in quantized steps, opening the possibility of treating the measured central charge not as a fixed label but as an experimentally addressable piecewise-quantized quantity. We then focus on the fractional quantum Hall effect (FQHE), where the chiral central charge c− directly governs the quantized thermal Hall conductance. After reviewing the role of edge conformal field theories and current bounds on thermal transport, we propose experimental modifications—such as engineering multi-component edge states, coupling to non-Abelian quasiparticles, or introducing controlled categorical perturbations—that could render higher coherence breakdown detectable as shifts in the effective central charge. Two further elements complete the program. First, we show that within the consistent framework, all route- and bracketing-dependent observables vanish identically (route blindness), so that the pentagon and hexagon interferometers and thermal Y-junction networks we design operate as precision null tests of the modular-functor axioms themselves—the axioms stating that anyonic amplitudes are determined by the topology of a process rather than by the bookkeeping route used to compose it. Second, we show that a quantized remnant of route sensitivity survives in exactly one consistent form: the holonomy of closed cycles of categorical controls, realizing a central-charge pump for which the integer count per cycle is a family invariant beyond any static stacking description. The resulting framework provides both a conceptual reinterpretation of the central charge as a higher obstruction in categorical terms and a concrete experimental route for probing its dynamical behavior. Beyond the quantum Hall setting, these ideas suggest a broader program: anomalies, topological phases, and even string worldsheet central charges may admit reinterpretation through higher coherence. We conclude by outlining a research agenda in which categorical methods yield new experimental observables, potentially transforming the interplay between mathematics, condensed matter physics, and high-energy theory.

Quantum Reports doi: 10.3390/quantum8030062

Authors: Victoria Mellor Fahad Ahmad

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family {Fk} is defined by Fk(q)=∇Sk(q), the gradient of the generating function of a secret Lagrangian submanifold Lk on the symplectic torus T2n. The key k specifies a composition of kicked-rotor maps in the strongly chaotic regime, whose classical Lyapunov exponents grow as log(K/2) per kick. The HPRF is best understood as a seeded one-way function with high min-entropy output: Fk is smooth (C∞), so its raw output is not directly usable as a uniform keystream, but it is computationally hard to invert. We construct three symmetric encryption modes—Mode A (key-dependent coordinate frame), Mode C (Lagrangian keystream), and Mode AC (hybrid)—in which the HPRF supplies the hardness and a key derivation function (HKDF) supplies bit-level uniformity. Standard symmetric composition then yields IND-CPA and IND-CCA2 security. Classical security reduces to the Lagrangian identification problem (LIP), shown as equivalent to the Hamiltonian inversion problem of recovering the kick parameters, which we state as an explicit hardness assumption supported by a precision/sample-complexity obstruction from the positive Lyapunov exponents, by the empirical failure of concrete attacks, and (more heuristically) by topological suggestiveness from the Arnold conjecture and Floer theory. We validate a gradient-fitting attack and an algebraic-structure attack and show that both fail. For quantum security, we propose what we believe is the right framing: that the composed Floquet operator U^Kr is a candidate pseudorandom unitary (PRU) in the sense of Ji–Liu–Song. We provide three independent pillars of evidence—Wigner–Dyson spectral statistics, Lyapunov-rate scrambling, and conjectural approximate-design behaviour—and reduce the HPRF quantum security to the PRU conjecture for U^Kr. We then retire the dynamical-localisation argument of previous drafts as inapplicable at cryptographic parameters; the chaotic-pseudorandomness regime that the operator actually inhabits is, we argue, a stronger foundation than the one that localisation would have provided. A deterministic fixed-point arithmetic core ensures cross-platform bit-exact consistency. A reference implementation validates correctness across all modes, and an NIST SP 800-90B analysis of the output min-entropy fixes the parameter sets. As a foundational proposal, the HPRF is intended for settings that seek a symmetric hardness assumption structurally independent of the algebraic problems underlying current cryptography, for example, as a hedge primitive in defence-in-depth designs, or as a basis for further study of geometry- and chaos-based cryptography, rather than as a drop-in replacement for AES or lattice-based schemes at this stage.

Quantum Reports doi: 10.3390/quantum8030061

Authors: Camilla Maria Kyllikki Josephson

We characterize when exponential reweightings of a no-signalling CHSH probability box preserve no-signalling. While such tilts are automatically positive and normalized within each measurement setting, they can modify cross-setting marginals and thereby introduce signalling into the probability table. We identify a four-dimensional setting-only redundancy in the residual parametrization, derive the exact nonlinear compatibility conditions for no-signalling preservation, and obtain the linearized no-signalling constraint around a no-signalling reference box. For the unbiased Tsirelson CHSH box, we compute the linearized constraint in closed form and show that the admissible tangent space has dimension twelve before quotienting and dimension eight after quotienting by the setting-only redundancy, matching the standard dimension of binary no-signalling boxes. Exact-probability calculations confirm the predicted scaling: generic residual directions produce first-order no-signalling leakage, while admissible tangent directions suppress the leakage to second order. We further show that local-additive residuals, despite their algebraic locality, are not generically no-signalling safe. These results give a sharp first-order admissibility criterion for exponential tilts of Bell probability boxes.

Quantum Reports doi: 10.3390/quantum8030060

Authors: Alan Abraham-Mexicano Carlos V. Muro-Medina Valentin Flores-Payan Elisa Ramos-Pinzon Carolina L. Recio-Colmenares Roxana B. Recio-Colmenares Cesar A. Garcia-Garcia

The Rio Santiago basin is one of the most environmentally stressed river systems in Mexico, with persistent organic, nutrient, microbial, surfactant, and metal contamination. This study develops a near-term quantum machine learning workflow for environmental monitoring and water-pollution profiling using multivariate records from 13 stations between 2009 and 2022. QML is evaluated here because quantum feature maps can define nonlinear, interaction-rich kernels that remain executable on present quantum hardware, providing an alternative representation to compare with classical PCA, RBF, UMAP, and HDBSCAN baselines rather than a presumed computational advantage. After quality screening, log transformation, standardization, and domain-guided feature selection, pollution profiles are evaluated across PCA, RBF spectral clustering, UMAP/KMeans, UMAP/HDBSCAN, a simulated ZZ-style quantum feature-map kernel, and Qiskit Runtime hardware evaluations of the same kernel concept. The initial cleaned-data results show that classical PCA clustering identifies broad lower-load, high organic/surfactant, and rain-season solids/microbial profiles. UMAP/HDBSCAN provides the strongest cleaned full-sample nonlinear baseline, with a silhouette score of 0.568 after excluding 177 noise samples. The simulated quantum-kernel representation separates station-linked gradients, while matched n = 650 stability diagnostics show near-identical quantum-kernel clustering across random initializations (mean ARI = 0.994 for cleaned data) but retain the RBF kernel as the strongest nonlinear comparator. Two 24-sample Qiskit hardware runs and two matched 8-record hardware checks provide proof-of-execution evidence. The analysis is framed as a controlled representation study, not as a claim of quantum advantage.

Quantum Reports doi: 10.3390/quantum8030059

Authors: Carlos Gabriel Rondon De Vivo

We propose a foundational framework in which internal temporal ordering, the low-entropy boundary of the observable branch, the compatibility of a local thermodynamic arrow with a global partition lifecycle, and a qualitative late-time dark-energy sign relation are organized as projections of a single internal-access architecture. The observable universe is treated as an internally accessible partition of a larger pure atemporal quantum state satisfying the Wheeler–DeWitt constraint. The ordering parameter is not identified with partition entropy itself; it is interpreted as an algebraic readout-depth parameter associated with a nested tower of admissible factor-like subalgebras, each inclusion adding one unit of autonomous distinguishability to the accessible sector. The reduced entropy S(rho_S) is then the Page-like scalar profile evaluated along this depth. This separates the internal ordering structure from the entropy being measured while retaining Page complementarity between accessible and inaccessible capacities. A minimal cosmological bridge is introduced: in the semiclassical Friedmann–Lemaitre–Robertson–Walker regime, if the effective Hubble rate is monotonic in partition entropy and readout depth is monotonically oriented with observer time, standard kinematics imply a sign correspondence between entropy change and the effective dark-energy equation of state. The metric map remains open.

Quantum Reports doi: 10.3390/quantum8030058

Authors: Anibal Alviz-Meza Alejandro Valencia-Arias Félix Díaz Segundo Rojas-Flores

Lead isotope ratios are frequently used in archaeometric provenance analysis; however, the overlap of isotopic fields within the Andean metallogenic belt complicates reliable provenance determination. This study presents a reproducible fidelity-based kernel method for the unsupervised clustering of Andean lead-isotope data and investigates whether a quantum-mechanical similarity space can reveal geologically significant structures beyond the classical Euclidean partition. A dataset of 1522 measurements of 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb was analyzed using a fidelity-based quantum kernel based on a three-qubit Pauli feature map and compared with classical K-means clustering, Gaussian mixture models, and Ward’s agglomerative clustering under various preprocessing strategies and cluster counts. The optimal quantum kernel setup achieved the highest silhouette score at k = 2. However, because analytical uncertainties were not consistently reported across all the compiled sources, an uncertainty-weighted similarity could not be applied. Geological insights indicate that this binary division separates less radiogenic, arc-related compositions from more radiogenic and thorogenic crustal signatures, a contrast that broadly follows the west-to-east crustal-contamination gradient across the Andes. Conversely, the traditional four-cluster approach provides more detailed subdivisions that align with the previously identified isotopic provinces. The reported separation reflects the geometry of the quantum feature space rather than any hardware-level speed-up, as this work represents only a simulation approach. Overall, these findings support a hierarchical and complementary approach to analyzing Pb isotope origins, in which quantum kernel clustering provides robust large-scale separation and classical clustering enhances regional understanding.

Quantum Reports doi: 10.3390/quantum8030057

Authors: Bryan Sanctuary

We thank Vrba for the careful and constructive analysis of bivector spin [...]

Quantum Reports doi: 10.3390/quantum8020056

Authors: Anton Lorenz Vrba

This comment examines the mathematical framework developed by Bryan Sanctuary across a series of papers and preprints (2023–2025) concerning bivector and quaternion representations of spin and claims regarding Bell correlations. We focus on the internal algebraic structure, the treatment of measurement correlations, and the use of linear combinations of projections from a single global bivector. We find that the framework is internally consistent, preserves positivity of expectation values, and produces correlations resembling the quantum correlation −a·b. These correlations are generated using a shared global algebraic object rather than from ±1-valued random variables satisfying the locality and factorization hypotheses of Bell’s non-existence theorem. Consequently, the results are best understood as describing a non-trivial classical geometric framework that lies outside the scope of Bell’s theorem, rather than as a contradiction of it. The analysis is restricted to mathematical and probabilistic considerations, without reference to physical or experimental interpretations.

Quantum Reports doi: 10.3390/quantum8020055

Authors: Bohan Zhang

We develop the binary-shadow method for exact CNOT counting and apply it to arbitrary wire permutations. The Heisenberg evolution of rotated local Z observables converts every CNOT gate into an elementary transvection over F2, and for a wire permutation, the resulting binary shadow is rigid: it must equal the associated permutation matrix. This reduces the exact CNOT cost of a wire permutation in the CNOT+local model to the transvection length of its permutation matrix. The remaining problem is classical. The relevant mathematical input is the transvection-length theory of permutation matrices, or equivalently, the CNOT-only synthesis of permutation circuits. Combining the binary-shadow reduction with the graph-theoretic link-middle-cut theorem for cycle matrices yields an exact formula: if σ∈Sn has c(σ) disjoint cycles, then CNOT-cost(Wσ)=ℓtr(Pσ)=3n−c(σ). The novelty is therefore not the CNOT-only permutation formula by itself, but the transfer of that exact lower bound to the CNOT+local model: arbitrary one-qubit gates may rotate the local Pauli axes, but they cannot reduce the CNOT count of a wire permutation. In particular, the n-qubit cyclic SWAP gate Sn|x1⟩1|x2⟩2⋯|xn⟩n=|xn⟩1|x1⟩2⋯|xn−1⟩n requires exactly 3(n−1) CNOT gates, even when arbitrary one-qubit gates are allowed at zero cost. Thus, the exact values for n=2,3,4,5,6,… are 3,6,9,12,15,…. We also give explicit optimal factorizations for n=4 and n=5, and show more generally that each additional wire in a cyclic shift costs exactly three more CNOT gates.

Quantum Reports doi: 10.3390/quantum8020054

Authors: Seyedeh Aram Salehi Hanieh Naderi Seyyed Amir Asghari Javad Chaharlang Yvon Savaria

This paper reviews hybrid quantum–classical (HQC) architectures for COVID-19-related respiratory medical-image analysis. To address the heterogeneity of existing studies, we propose an architecture-centric taxonomy based on the functional role and placement of the quantum module. Reviewed models are grouped into three archetypes: Archetype A, where quantum circuits act as patch-level quanvolutional preprocessors; Archetype B, where classical feature extractors are coupled with quantum classifier heads; and Archetype C, where quantum circuits generate intermediate features for downstream classical classifiers. Ten peer-reviewed journal studies were selected through a PRISMA-inspired search and analyzed across architecture, diagnostic performance, quantum resource reporting, validation rigor, computational scalability, and deployment feasibility. The review shows that HQC models often report promising binary COVID-19 screening results on CT or chest X-ray images, but multiclass respiratory classification remains less stable. Key limitations include simulator-dominated evaluation, limited external validation, unclear patient-wise splitting, incomplete reporting of qubit counts, circuit depth, and shots, and insufficient comparison with strong classical baselines. Overall, current HQC models should be viewed as exploratory quantum-augmented classical pipelines rather than clinically validated diagnostic systems. No conclusive task-level quantum advantage has yet been demonstrated for COVID-19 medical imaging. Future progress requires standardized benchmarking, transparent quantum-resource reporting, patient-wise and multi-center validation, hardware-aware evaluation, and interpretable hybrid designs compatible with NISQ-era constraints.

Quantum Reports doi: 10.3390/quantum8020053

Authors: Lorenzo Albanese

Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of interior degrees of freedom and horizon correlations. In this work, the regular black-hole geometry introduced by Dymnikova is used as a compact, single-scale effective background for black-hole quantum information considerations. The aim is not to propose a new regular metric but to clarify how an established finite-core geometry can support a nonsingular description of the Schwarzschild interior at the effective level. The geometry preserves the Schwarzschild asymptotic limit while replacing the divergent central region with a finite de Sitter-like core. The curvature invariants remain finite, and the effective source admits an anisotropic-fluid interpretation whose central limit is isotropic and vacuum-like. This use therefore provides a minimal geometric setting, rather than a newly proposed metric solution, for discussing nonsingular black-hole interiors. It does not establish unitary evaporation, information recovery, dynamical stability, or a microscopic quantum-gravity mechanism. Instead, it identifies a finite-curvature spacetime framework in which questions concerning interior quantum degrees of freedom and horizon entanglement can be formulated without encountering a curvature singularity.

Quantum Reports doi: 10.3390/quantum8020052

Authors: Horace T. Crogman

Quantum processes with indefinite causal order challenge the classical assumption that operations must occur in a single fixed temporal sequence. The quantum switch provides a concrete setting in which two operation orders, A≺B and B≺A, are coherently controlled by a quantum system. In the strict process matrix formulation of the lazy guess your neighbour’s input (LGYNI) game, however, quantum theory, including the quantum switch, does not violate the standard causal inequality when probabilities are computed solely from local instruments. In this work, we study an extended control-assisted operational protocol in which the control system of the quantum switch is measured and used to define the task output. We compare increasingly expressive strategy classes, including single-qubit SU(2) operations, product target-ancilla operations, and entangling Cartan-decomposed two-qubit operations with generalized POVMs. Restricted models saturate or remain below the 3/4 fixed-order benchmark, whereas the optimized Cartan + ancilla + POVM strategy reaches Psuccext≈0.83596, demonstrating enhanced task performance within the extended protocol. The optimized strategy remains operationally no-signaling to numerical precision and retains its extended protocol advantage under more than 25% white noise admixture. These results identify the operational resources required for control-assisted quantum switch enhancement and support the view that indefinite temporal order can be used as a quantum informational resource without implying a breakdown of operational causality.

Quantum Reports doi: 10.3390/quantum8020051

Authors: Konstantinos Prousalis Dimitris Ntalaperas Konstantinos Georgiou Andreas Kalogeropoulos Thanos G. Stavropoulos Theodora Karamanidou Christos Papalitsas Lefteris Angelis Nikos Konofaos

A novel quantum algorithm for biological sequence alignment is presented and analyzed. The large volumes of data generated through genome sequencing, de novo assembly, resequencing, and transcriptome sequencing at the DNA and RNA levels foreshadow the growing demand for higher computational power and more sophisticated alignment methodologies. The rapid advancement of modern sequencing technologies in genomics has motivated the reconsideration of existing approaches for the design and implementation of alignment protocols. Emerging quantum computing accelerators may provide transformative solutions in this domain as quantum hardware progressively reaches higher levels of gate-operation maturity. This work proposes a computer-vision-based approach that exploits the unique properties of quantum entanglement within a dot-matrix representation to address the increasing demand for efficient processing of biological data. A quantum-accelerated protocol is developed and evaluated using the Qiskit software framework of IBM. Runtime experiments support the potential of the proposed methodology to provide advantageous sequence-alignment performance in terms of accuracy, completeness, and computational complexity. The system is evaluated under multiple operational conditions and demonstrates promising performance advantages.

Quantum Reports doi: 10.3390/quantum8020050

Authors: Dimitrios Pourikas Konstantinos Prousalis Nikos Konofaos

Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.

Quantum Reports doi: 10.3390/quantum8020049

Authors: Bin Li

We propose a structural framework for interpreting quantum computational advantage in terms of admissible continuation of configurations. In this framework, a quantum computation is described not only as a sequence of gates acting on a state vector but also as the organization of admissible histories whose phase contributions combine coherently in a manner related to sum-over-histories and path-integral formulations of quantum mechanics. We identify three structural features that are relevant to quantum advantage: the multiplicity of admissible histories, the degree of phase coherence among them, and the non-factorizable structure of continuation constraints corresponding to entanglement-like global dependence. To make these features explicit, we introduce the notion of effective coherent multiplicity, which measures the coherently usable portion of an admissible-history space before probability normalization. We then formulate a structural speedup conjecture: substantial quantum advantage requires not merely a large number of possible histories but scalable coherent multiplicity supported by non-factorizable constraints whose instability remains bounded. We also introduce a coherent-fiber criterion, which identifies phase-alignable families of histories selected by compact computational relations as a structural source of coherent amplification. This formulation does not replace standard complexity-theoretic measures such as circuit size, query complexity, or BQP membership. Rather, it provides a complementary structural language for relating those measures to interference, entanglement, decoherence, and the organization of computational history space. The framework clarifies, at a structural level, why raw branching alone is insufficient for speedup, why unstructured search yields only a limited advantage, and why problems with compact global regularities, such as Simon’s problem and period finding, can support stronger coherent amplification. The paper also discusses how the proposed quantities relate to standard notions, including success amplitudes, entanglement measures, tensor-network simulability, and fault-tolerance constraints. In this way, admissible-history structure is presented as a diagnostic viewpoint for understanding both the power and limitations of quantum computation.

Quantum Reports doi: 10.3390/quantum8020048

Authors: Angelo Plastino

We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability. The approach is based on the quantum relative entropy and the quantum Fisher information metric, which together induce a natural Riemannian geometry on the manifold of quantum states. Using the second-order expansion of relative entropy, we show how the Fisher metric governs the local structure of distinguishability between nearby states and defines a corresponding thermodynamic length. This geometric structure provides an effective description of finite quantum state transitions in terms of fluctuation geometry and information-space distance. The formalism is applied to thermal two-level systems and harmonic oscillator states, illustrating how the Fisher metric encodes susceptibilities, fluctuations, and geometric transition costs. We also discuss the relation between thermodynamic length, dissipation bounds, and optimal paths in state space. Within this framework, wave function collapse is interpreted not as a microscopic dynamical mechanism, but as an effective state-update process that admits a geometric characterization in the manifold of density operators. The resulting perspective unifies concepts from quantum information theory, thermodynamics, and differential geometry within a common operational framework based on statistical distinguishability. Possible connections with quantum speed limits, entanglement geometry, and holographic relations between relative entropy and gravitational dynamics are briefly discussed.

Quantum Reports doi: 10.3390/quantum8020047

Authors: Doron Kwiat

We introduce a local phase-field framework for spin-entanglement correlations. In this framework, the relevant hidden variable is an internal scalar phase associated with each fermion and derived from two underlying real fields. The fields are assumed to evolve locally in ordinary spacetime. When a particle pair is produced at a common spacetime event, the pair acquires a shared phase-locking condition at creation; after separation, the two internal phases evolve independently and no nonlocal interaction is introduced. Spin measurements by Stern–Gerlach analyzers are modeled as local filtering operations. Each local response depends only on the internal phase carried by the particle and on the orientation of the local analyzer. The local response function A(α,λ) = cos(λ − 2α) is derived from the spinorial transformation law of the underlying real field pair and the projection geometry of the detector interaction; it is not a phenomenological ansatz. From these deterministic local responses we derive an analog correlator. The raw product moment of the continuous detector outputs evaluates to ⟨AB⟩ = −½ cos 2(α − β), which satisfies classical Clauser-Horne-Shimony-Holt (CHSH) bounds. After Pearson normalization—the operationally appropriate correlation measure for continuous analog detector outputs, justified by channel-contrast physics and scale invariance—the normalized correlator yields E(α,β) = −cos 2(α − β), matching the quantum singlet correlator in functional form. When this normalized correlator is inserted into the CHSH expression, it yields the numerical value 2√2. This result is a structural consequence of the reduced marginal variance of continuous response functions relative to the unit-variance dichotomic observables assumed in Bell’s derivation; it does not constitute a violation of Bell’s inequality. The model does not reproduce quantum singlet statistics at the level of binary detector outcomes, where the correlator takes a triangular rather than cosine form. The contribution is therefore ontological and conceptual rather than predictive. The framework preserves parameter independence and no-signaling throughout. It provides a concrete real-field ontology for spin correlations based on internal phase structure, and it demonstrates that the functional form of the quantum singlet correlation can be obtained from a strictly local deterministic description, provided that the detector responses are treated as continuous analog quantities and normalized accordingly. We compare the model with earlier phase-based approaches and discuss experimental configurations—including time-resolved and multi-stage Stern–Gerlach measurements—that could in principle probe the proposed internal-phase dynamics at the pre-registration level.

Quantum Reports doi: 10.3390/quantum8020046

Authors: Vrushali Nikam Trupti Atre Lavanya Santhosh Asha Konasagara Nagaraja Praveena Mydolalu Veerappa

Quantum image processing provides significant storage benefits over classical methods. However, current quantum image representation techniques exhibit limitations regarding encoding efficiency, circuit complexity, and adaptability to image content. This paper proposes Saliency-Aware Hybrid Quantum Image Representation (SAHQR), utilizing saliency detection for content-adaptive representation. It selectively focuses on salient regions, allocating quantum resources proportionally to visual importance, whereas existing techniques represent all regions uniformly.The proposed approach is evaluated against ten state-of-the-art quantum image representation techniques using ten criteria: number of qubits, circuit depth, gate complexity, encoding time, scalability, information loss, compression ratio, memory overhead, and implementation complexity Experimental results on 6097 medical images from the MINC database demonstrate that this work should be interpreted as a proof of concept for saliency-aware quantum encoding, rather than as a universally optimal representation.The evaluation is extended to 2000 Synthetic Aperture Radar (SAR) tiles and 2298 Brain Tumor MRI scans to validate cross-domain generalization. Statistical significance tests (p < 0.001) confirm SAHQR yields statistically significant improvements over existing techniques across all three domains.

Quantum Reports doi: 10.3390/quantum8020045

Authors: Boxuan Wu Lei Wang

Quantum finance represents a pivotal and cutting-edge application domain within the burgeoning field of quantum computing. In this work, we propose a two-step quantum approximate optimization algorithm (two-step QAOA) for portfolio optimization and risk assessment. The algorithm initiates by formulating the stock selection problem as a quadratic unconstrained binary optimization (QUBO) problem and employs a classical-quantum hybrid method to find the ground state of the Hamiltonian. We then introduce an energy-based characteristic indicator U∈[0,1), which quantitatively evaluates portfolio performance under customizable investment preferences, effectively capturing the trade-off between expected return and risk. The number of qubits required scales with the number of stocks N in the pool, and the number of Hamiltonian terms is O(N2). Numerical simulations show that the algorithm provides consistent and reasonable assessment results on both training and test datasets under different investment preferences (aggressive or conservative), validating the capability of the characteristic indicator to extract intrinsic information from the portfolios. Additionally, by incorporating warm-starting and digitized counterdiabatic techniques, the algorithm achieves improved scalability and faster convergence. Our work presents a flexible and practical algorithmic framework for applying quantum computing in the financial domain.

Quantum Reports doi: 10.3390/quantum8020044

Authors: Jérôme Beau

Violations of Bell inequalities are commonly interpreted as evidence for nonlocal influences or as constraints on realist descriptions. We show that the failure of Bell-type factorizability arises naturally when observable outcomes are obtained through a non-injective mapping from an underlying configuration space. In this setting, the standard factorization assumption can be viewed as an implicit requirement that observable variables admit a jointly factorizable completion at the underlying level. We demonstrate that this requirement need not hold when the mapping from underlying configurations to observables is many-to-one. The resulting breakdown of probabilistic factorization does not rely on superluminal dynamics or hidden causal influences, but follows from information loss under projection. Observable outcomes correspond to equivalence classes of underlying configurations, preventing the assignment of independent local variables. We illustrate this mechanism with an explicit toy model producing Bell–CHSH violations while preserving operational no-signalling and statistical independence of measurement settings. The model is not intended to reproduce quantum correlations quantitatively, and may exceed the Tsirelson bound; its role is to isolate the structural origin of the violation. This analysis does not contradict Bell’s theorem, but identifies a class of effective descriptions for which its factorizability assumption does not apply. The framework preserves locality at the underlying level, introduces no additional hidden-variable dynamics, and does not modify quantum mechanics. It clarifies how classical factorization is recovered in regimes where the effective mapping becomes approximately injective. In the operator language of quantum theory, the same mechanism admits a natural reformulation in terms of reduction to an effective observable subalgebra by a noncommutative conditional expectation.

Quantum Reports doi: 10.3390/quantum8020043

Authors: Stefan Evans Joanna N. Ptasinski

We analyze noise in a quantum-enhanced fiber optic gyroscope (FOG), focusing on one of the leading sources of phase uncertainty—uncorrelated photon saturation. Taking a squeezed state input as a source for N00N states, we compute the uncorrelated false coincidence counts at the optimal phase bias and determine an upper limit to the squeezed amplitude ξ which allows for sub-shot noise precision. As examples, we apply parameters of present-day quantum FOG experiments and determine the maximum possible precision enhancement based on their respective ξ and optimal phase bias points. With the aim of supporting future FOG setups with higher N00N state fluxes, our result highlights the need to transition to multimode states to bypass the ξ limitation, such as photon pairs generated by the dynamical Casimir effect.

Quantum Reports doi: 10.3390/quantum8020042

Authors: Riccardo Fantoni

In this paper, we review the physics of many bodies in the context of general relativity. Starting from the stress–energy tensor for one body and moving onto those for a swarm of bodies and for a perfect fluid, we review the relativistic hydrodynamics, kinetic theory, and statistical physics of N identical bodies. We conclude our excursion with a thermal equivalence principle in physics.

Quantum Reports doi: 10.3390/quantum8020041

Authors: Xinyue Li Yan-Han Yang Ming-Xing Luo

This work proposes an extended Mermin inequality based on a hybrid classical model that involves only one classical source, with the remaining sources being post-quantum. In a chain-structured quantum network consisting of hybrid Einstein–Podolsky–Rosen (EPR) pairs and Greenberger–Horne–Zeilinger (GHZ) states, joint measurements are performed at the central node, while local measurements are conducted at the peripheral nodes. This setup shows that the obtained quantum correlations can violate the proposed inequality with fewer measurement settings, thereby verifying network nonlocality. Furthermore, we extend this method to chain networks of arbitrary length n and show that the proposed inequality remains effective in verifying network nonlocality.

Quantum Reports doi: 10.3390/quantum8020040

Authors: Mohammad Mohammadiaria

Controlling spin dynamics conventionally requires external magnetic fields, strong electric bias, or material-specific spin–orbit interactions, while the temporal reference frame remains fixed. Here we introduce curved-time spintronics, a framework in which a synthetic lapse field, implemented through GHz surface-acoustic-wave (SAW) modulation, reshapes the effective flow of time experienced by spinor, magnonic, and photon–spin degrees of freedom. Using a curved-time Schrödinger–Pauli model, we show that it renormalizes the Larmor frequency, modifies SOC-driven splittings, and produces helicity-dependent spin precession under circularly polarized excitation. Strikingly, a spatial lapse gradient induces a Hall-like transverse drift even when in the absence of any external electric field or intrinsic Berry curvature, demonstrating that time geometry alone can generate transverse transport. Time-domain simulations confirm curvature-driven Hall response across graphene, carbon nanotubes, and generic Dirac platforms, establishing a material-agnostic, field-free mechanism for transverse spin manipulation. We further predict curvature-dependent spin diffusion, temporal magnon focusing, and helicity-selective entanglement generation, and propose pump–probe detection via ultrafast Kerr rotation synchronized to SAW-driven lapse modulation. These results position engineered time geometry as a new spintronic control axis, enabling Hall-like effects, spin transport, and chiral phase manipulation without relying on intrinsic material properties, magnetic fields, or electric gating.

Quantum Reports doi: 10.3390/quantum8020039

Authors: Ting Zhou

Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals that its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving the gradual attenuation of light intensity down to the single-photon regime and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.

Quantum Reports doi: 10.3390/quantum8020038

Authors: Robert Castro

Variational models describe deformation and stability through the first and second variations in an underlying functional, but the relationship between these responses is seldom expressed as an intrinsic equilibrium quantity of the model itself. A canonical curvature–strain representation for equilibrium ratios arising in variational field settings is developed. For a twice Fréchet differentiable functional and an admissible perturbation generator, strain is defined as normalized first-order response and curvature as normalized second-order response along the generator direction. Their quotient defines a curvature–strain ratio that measures proportional balance between deformation and curvature within the model. The main result shows that this curvature–strain ratio is a canonical representative of a response ratio already implicit in the variational data. Under canonical normalization, the curvature–strain ratio coincides with the quotient of second- and first-order response, and stationarity of the curvature–strain ratio is equivalent to proportional stationarity of that response quotient along the admissible flow. A further theorem establishes transfer of local isolation: when the second-variation operator satisfies standard hypotheses such as compact resolvent and non-degeneracy of the constrained extremum, isolated equilibrium ratios persist in the curvature–strain representation for the same operator-theoretic reasons. Quadratic scalar and Maxwell-type models illustrate the construction. The paper establishes a mathematically controlled curvature–strain representation of equilibrium ratios within ordinary variational theory, with emphasis on the analysis of variational response and equilibrium balance.

Quantum Reports doi: 10.3390/quantum8020037

Authors: Vrushali Nikam Shirish Sane Manish Motghare

Quantum image representation (QIR) is the basic idea behind quantum image processing. It explains how a normal image is converted into quantum states so that it can be processed using quantum computers. The commonly used models for QIR are Flexible Representation of Quantum Images (FRQIs) and Novel Enhanced Quantum Representation (NEQR). Though these approaches highlight the potential of quantum-based image encoding, the limitation of practical applicability on Noisy Intermediate-Scale Quantum (NISQ) devices exists. In this paper, we propose an intensity-preserving quantum image representation (IP-QIR) scheme that aims to maintain accurate grayscale intensity information while significantly reducing quantum resource usage. The proposed method employs a controlled rotation-based encoding strategy, where pixel intensities are embedded into the measurement probability of a single intensity qubit, and spatial information is represented using position qubits. To further enhance feasibility on near-term quantum hardware, the framework operates on small image patches instead of full-resolution images, thereby reducing circuit depth and overall complexity. The performance of the proposed IP-QIR approach is evaluated through IBM Qiskit simulations on three types of grayscale images: synthetic image patches, synthetic aperture radar (SAR) images, and medical tuberculosis (TB) chest X-ray images. Experimental results demonstrate that IP-QIR achieves better intensity preservation than FRQIs and NEQR, with fidelity values reaching up to 84.12% for both SAR and medical datasets. In addition, IP-QIR represents a 4×4 image patch using only five qubits, which significantly reduces the qubit requirement when compared to NEQR, while still preserving high reconstruction accuracy.

Quantum Reports doi: 10.3390/quantum8020036

Authors: Wen-Ran Zhang Hengyu Zhang

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence.

Quantum Reports doi: 10.3390/quantum8020035

Authors: Ghenadie N. Mardari

A classical fluid splitter produces the same patterns of energy redistribution as a Stern–Gerlach quantum device, with rotationally invariant coefficients of correlation between molecular paths. Alternative settings express a cosine squared relationship, leading to Tsirelson-type Bell violations with outcome independence. This result confirms the Correspondence Principle of quantum mechanics, where individual detection events express system-level properties according to Born’s Rule. Kochen–Specker contextuality and Bell Locality are not formally contradicted, but their interpretation is in question. Current definitions of “Local Realism” are limited to intrinsic particle properties. In contrast, quantum-like correlations require the acknowledgement of ensemble effects on dynamically inseparable entities, even when those entities are observed one at a time.

Quantum Reports doi: 10.3390/quantum8020034

Authors: Freeman Hui

We present Quantum-Informational History Optimization Theory (QIHOT) as a formal proposal for selecting a single realized quantum history from a space of dynamically admissible histories subject to boundary constraints. In the present paper, we restrict attention to finite-dimensional and toy-model settings, where the framework can be stated explicitly. QIHOT separates two levels: a dynamical prior over admissible histories generated by standard quantum evolution, and an informational selection rule that reweights those histories by an entropy-based cost functional. Within this structure, we show that standard Born statistics are recovered in symmetric-cost measurement scenarios when the prior is the usual Hilbert-space quantum prior. We further formulate conditions under which operational no-signaling is preserved, provided the selection functional factorizes locally for spacelike-separated regions. A fully worked two-outcome model illustrates how the framework interpolates between coherent evolution and measurement-like branch selection. We contrast QIHOT with the Many-Worlds Interpretation, the Transactional Interpretation, the Consistent Histories formalism, the Schwinger–Keldysh formalism, and Lagrangian-based retrocausal models, highlighting structural similarities and key differences. We emphasize that the present paper develops QIHOT as a scoped formal proposal with partial consistency results rather than as a complete replacement for quantum theory. Possible extensions to consciousness and cosmology are deferred to brief outlook-level discussion.

Quantum Reports doi: 10.3390/quantum8020033

Authors: Mohamed Sacha

We formulate the Quantum Information Copy Time (QICT) framework for conserved charges under strictly local quantum dynamics and isolate its logically strongest consequence. The theorem-level core is a receiver-optimised variational speed-limit inequality: after projection away from the conserved zero mode, the copy time is bounded from below by the inverse square root of a Liouvillian-squared receiver susceptibility times a local encoding seminorm. This statement is written in a finite-volume operator framework and does not require a diffusive ansatz. We then examine what follows only after additional infrared assumptions. Under a single diffusive slow-mode hypothesis, the variational inequality reduces to the practical scaling relation used in the benchmark computations. That reduction is treated as conditional and is stress-tested numerically rather than promoted by rhetoric. Within the anomaly-free Abelian span relevant for one Standard-Model-like generation, hypercharge selection is elevated to theorem-level status; by contrast, minimal gauge-algebra uniqueness remains explicitly conditional on additional model-selection axioms. The remainder of the manuscript is organised as an explicitly documented closure programme built on top of this core. In that closure, a gauge-coded QCA construction, a microscopic benchmark for the transport normalisation, and an electroweak matching convention are combined to produce a resonance-centred Higgs-portal singlet-scalar mass band together with direct-detection, invisible-width, and relic-consistency checks. These latter results are presented as model-dependent consequences of an explicit closure ansatz rather than as deductions from locality alone.

Quantum Reports doi: 10.3390/quantum8020032

Authors: Wan Zheng

The emergence of classicality through quantum decoherence is commonly described from complementary perspectives emphasizing stability (environment-induced superselection), objectivity (Quantum Darwinism), or physical feasibility (information thermodynamics). In realistic open quantum systems, however, these aspects coexist and compete under finite physical resources. In this work we argue that classical structure selection is most naturally understood as a resource-constrained, multi-objective process. We introduce the Informational Economy Functional (IEF), an effective accounting framework that places loss of distinguishability, energetic dissipation, and the generation of redundantly accessible records on equal footing. The associated Principle of Informational Economy characterizes emergent classical structures as those achieving an optimal compromise among stability, objectivity, and energetic feasibility. Classicality is thus neither maximally stable, nor maximally redundant, nor maximally energy-efficient, but instead reflects a Pareto-optimal balance shaped by environmental constraints. The IEF yields falsifiable predictions concerning pointer-structure variability, redundancy deformation, and resource-sensitive trade-offs, and suggests concrete experimental tests in continuously monitored quantum platforms. Classical reality is thereby reinterpreted as the most economical configuration in which information can stably form, propagate, and persist.

Quantum Reports doi: 10.3390/quantum8020031

Authors: Jacob Yan Gurevich

We identify a fundamental tension between general relativity and spectral geometry arising from the global, nonlocal character of spectral data versus the local causal dynamics of spacetime. To resolve this, we postulate spectral invariance, δΛn=0, requiring the eigenvalues of the Laplace–Beltrami operator to remain fixed under physical evolution. This condition yields a compensatory relation between metric deformations and eigenfunction amplitudes, suggesting a kinematic coupling linking energy distribution to spacetime curvature. From the second variation of the associated energy functional, we derive a rank-4 tensor proportional to the inverse DeWitt supermetric on superspace and a contracted rank-2 tensor proportional to the spacetime metric, and we recover a invariance law of the energy functional in configuration space. Spectral invariance may suggest a framework in which geometry and energy are co-defined through fixed spectral data.

Quantum Reports doi: 10.3390/quantum8020030

Authors: Sean T. Crowe Joshua J. Leiter John P. T. Stenger Zachary L. Barvian Joseph A. Diaz Shoshana Kinzel Joanna N. Ptasinski Daniel Gunlycke

We present a new Python package that uses the formalism of geometric quantum complexity to numerically compute metric-dependent geometric cost and control functions associated with preparing a given unitary transformation on a quantum computer. The numerical procedure we implement is presented and discussed. Analyzed quantum circuits include: the quantum Fourier transform for up to four qubits, a random circuit with depth 100, and a circuit for analyzing the evolution of a fermionic chain with several lattice sites.

Quantum Reports doi: 10.3390/quantum8020029

Authors: Ke Zhang Hongyi Fan

The Wigner operator’s normal ordering form is deduced by using the method of integration within the ordered product of operators, and the operator’s Weyl ordering symbol is employed. The integration theory within the Weyl ordering product of operators is applied, and the Wigner operator’s Weyl ordering form is deduced. Then, the Wigner operator’s slice theorem is proposed, which helps project and display a new pure-state density operator. Thus, the quantization of classical tomography theory is realized. We illustrate the derivation of the bi- and tri-partite entangled state representations, respectively, which completes the argument.

Quantum Reports doi: 10.3390/quantum8020028

Authors: Jie Sun Zhimin Zhang Songfeng Lu

In this paper, we study two aspects of quantum adiabatic evolution for a prototypical search problem: the optimality of the corresponding algorithm and its relation to the quantum circuit model. Firstly, we propose a general framework for proving the square-root speedup of the quantum adiabatic algorithm to be optimal over classical computation, which is readily applicable to the case of multiple targets. Through this framework, we also find that it is possible to further reduce the time complexity by increasing the physical energy of the system, encompassing results from previous works. Secondly, we find that, on the one hand, when the quantum adiabatic algorithm that achieves quadratic speedup is implemented on a quantum circuit, the time slice needed is always consistent with its time complexity, which also encompasses previous results; on the other hand, however, if a further algorithmic improvement is considered, the time slice always remains invariant. This phenomenon represents a significant observation with potential applications. We anticipate that the main results of this paper will interest the quantum adiabatic computation community and may help us to design efficient quantum algorithms for practical problems in the future.

Quantum Reports doi: 10.3390/quantum8010027

Authors: Doron Kwiat

This work presents a classical theoretical framework in which combinatorial optimization emerges from the nonlinear relaxation of coupled real-valued phase fields governed by a global Lyapunov energy functional. Each computational element (CF-bit) evolves in a bistable periodic potential while pairwise interactions encode problem-specific couplings, enabling gradient-descent minimization of QUBO and Ising objective functions. The key contribution is an explicit global energy functional from which all dynamics are derived, guaranteeing monotonic energy descent under damping. This distinguishes the approach from several existing oscillator-based Ising architectures where the governing dynamics contain non-gradient terms and an explicit global Lyapunov functional has not been derived in their standard formulations. Numerical simulations on instances up to 20 bits demonstrate deterministic phase-locking convergence, with optional transient noise improving the exploration of rugged landscapes. While limited in scale and not overcoming NP-hardness, this work provides a conceptual framework showing how discrete optimization can emerge from continuous classical dynamics with a mathematically transparent energy structure.

Quantum Reports doi: 10.3390/quantum8010026

Authors: Manqoba Q. Hlatshwayo Manav Babel Dalila Islas-Sanchez Konstantinos Georgopoulos

Quantum computing has been rapidly evolving as a field, with innovations driven by industry, academia, and government institutions. The technology has the potential to accelerate computation for solving complex problems across multiple industrial sectors. Finance and economics, with many problems exhibiting computationally heavy requirements, comprise a high-profile sector where quantum computing could have a significant impact. Therefore, it is important to identify and understand to what extent the technology could find utility in the sector. This technical review is written for quantum applications researchers, quantitative analysts in finance and economics, and researchers in related mathematical sciences. It is divided into two parts: (i) a survey of quantum algorithms pertinent to problems in finance and economics, and (ii) mapping of several use cases in the sector to the potential quantum algorithms presented in part (i). We discuss some challenges on the pathway to achieving quantum advantage. Ultimately, this review aims to be a catalyst for interdisciplinary research that will accelerate the advent of the practical advantages of quantum technologies to solve complex problems in this sector.

Quantum Reports doi: 10.3390/quantum8010025

Authors: Felipe Bosa

This work presents the Theory of Spacetime Impedance (TSI), a phenomenological framework in which the vacuum is modeled as a distributed reactive medium with an effective RLC structure. At the classical level, the vacuum is characterized by permeability, μ0, permittivity, ε0, and impedance, Z0, so that the speed of light follows from the vacuum’s constitutive reactive properties. The TSI introduces a reactive–dissipative term, RH, as an effective mechanism associated with irreversibility, decoherence, and entropy production, providing a physical basis for the arrow of time. At the quantum level, TSI incorporates a quantum RLC triad associated with the electron, defined by quantum inductance, LK, quantum capacitance, CK, and von Klitzing resistance, RK. When normalized by the Compton wavelength, these quantities admit a direct comparison with μ0 and ε0, identifying the fine-structure constant as an impedance scaling factor between classical and quantum regimes. Within this unified reactive picture, inductive, capacitive, and resistive responses are respectively associated with gravitation, electromagnetism, and thermodynamic irreversibility, offering a complementary bridge across quantum, relativistic, and macroscopic domains.

Quantum Reports doi: 10.3390/quantum8010024

Authors: Eldar Sultanow Madjid Tehrani Siddhant Dutta William J. Buchanan Muhammad Shahbaz Khan

Quantum computing offers potential computational advantages, yet its integration into autonomous decision-making systems remains largely unexplored. This paper addresses the need for a unified framework that systematically combines quantum computation with agent-based artificial intelligence. We examine how quantum technologies can enhance the capabilities of autonomous agents and, conversely, how agentic AI can support the advancement of quantum systems. We analyze both directions of this synergy and present conceptual and technical foundations for future quantum–agentic platforms. Our work introduces a formal definition of quantum agents and outlines architectures that integrate quantum computing with agent-based systems. As concrete proof-of-concept implementations, we develop and evaluate three quantum agent prototypes: (i) a Grover-based decision agent for quantum search-driven action selection, (ii) a variational quantum reinforcement learning agent for adaptive policy learning in a multi-armed bandit setting, and (iii) an adaptive quantum image encryption agent that autonomously selects encryption strategies based on entropy-driven feedback. These prototypes demonstrate practical realizations of quantum agency in decision-making, learning, and security contexts under NISQ-era constraints. Furthermore, we discuss application domains including quantum-enhanced optimization, hybrid quantum–classical orchestration, autonomous quantum workflow management, and secure quantum information processing. By bridging these fields, we introduce a structured theoretical and architectural framework for quantum–agentic systems, providing formal definitions, system models, and early operational prototypes that illustrate the feasibility of quantum-enhanced agency under NISQ constraints.

Quantum Reports doi: 10.3390/quantum8010023

Authors: Robert Castro

We formulate a structural stability criterion for dimensionless physical constants within standard perturbative field frameworks. The analysis introduces a response-ratio functional Γ=κ/τ, defined from second-order sensitivity and first-order deformation measures associated with admissible variations in a field configuration. Stability is characterized by proportional stationarity of Γ, expressed as a first-order operator condition along transformation flows. The framework characterizes, within a declared variational model, when invariance of fixed constants can be represented as a stationarity condition. Under compactness and convexity assumptions typical of variational systems, stationary response ratios arise as isolated solutions of the associated operator equation; more general settings permit continuous spectra. Explicit functional definitions are provided within a conventional analytic setting, and the criterion is illustrated in representative classical field models. The results position proportional stationarity as a model-relative structural consistency condition for perturbative stability; isolation is conditional on compactness and non-degeneracy hypotheses, and continuous families may occur outside that regime. Limitations and possible extensions, including discretized spacetime formulations, are discussed.

Quantum Reports doi: 10.3390/quantum8010022

Authors: Rodolfo O. Esquivel Hazel Vázquez-Hernández Jonathan Ornelas-Muñoz

Here we perform a detailed information-theoretic (IT) analysis of atomic electron densities in the periodic table, from hydrogen (Z = 1) to lawrencium (Z = 103). By use of the Shannon entropy, the Fisher information and the disequilibrium functionals in both position and momentum spaces as fundamental descriptors of the atomic densities, the periodic table can be represented in a three-dimensional information space as a continuous, highly ordered manifold. The analysis shows that chemical periodicity naturally emerges as a helicoidal manifold (reminiscent of a helix) at the coordinates of a 3D theoretic-information space (Shannon, Fisher, Disequilibrium), with each period forming one segment within the continuous global trajectory. We find information-theoretic signatures of shell structure, sub-shell filling, and electron-configuration anomalies, such as the familiar irregularities seen in chromium and copper. Therefore, the helicoidal character emerges naturally and is not imposed a priori. Further, through the uncertainty principle of the complementary analysis in momentum space, more insights are gained by exposing maximal information-theoretic differentiation for lighter atoms and compression among heavy elements. Notably, momentum-space analysis reveals that hydrogen occupies a natural intermediate position between helium and lithium based on kinetic energy distribution—contrasting with IT position-space results that emphasize hydrogen’s unique delocalized electron density. Indeed, the 3D IT representation of the elements in position space aligns with the view that H does not belong to either the alkali metals or the halogens, but rather stands as a unique, standalone element. This complementary perspective provides new quantitative support for understanding hydrogen’s dual chemical nature, providing new quantitative insight into ongoing debates about hydrogen’s optimal periodic table position. Furthermore, by considering triadic relationships and complexity properties in relation to the López–Mancini–Ruiz (LMC) and Fisher–Shannon (FS) functionals, we show that atomic complexity increases monotonically along with nuclear charge, and we provide a quantitative measure of how organized atomic electron densities are distributed throughout the periodic system. Based on our IT analyses, the fundamental character of periodicity could be addressed by employing helicoidal representations that highlight the characteristics of hydrogen, while simultaneously preserving the autonomy of the blocks of elements.

Quantum Reports doi: 10.3390/quantum8010021

Authors: Hong Wang Jin Wang

Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave–particle duality can be interpreted as the uncertainty of spacetime for the particle. Summarizing all possible trajectories in conventional path integral quantum mechanics can be transformed into the summation of all possible spacetime metrics. Furthermore, we emphasize that in conventional quantum gravity, it is possible that the classical matter fields correspond to quantum spacetime. We argue that this is not quite reasonable and propose a new path integral quantum gravity model based on the new interpretation of wave–particle duality. In this model, the aforementioned drawback of conventional quantum gravity naturally disappears.

Quantum Reports doi: 10.3390/quantum8010020

Authors: Iñaki Del Amo Castillo

We present a covariant geometric extension of General Relativity formulated within a controlled effective field theory framework. The gravitational action is supplemented by curvature-dependent operators parametrized by three coefficients α, β, and γ, chosen such that the resulting field equations remain second order in time derivatives and free of Ostrogradsky instabilities. In a homogeneous and isotropic cosmological background, the modified dynamics generically replaces the classical Big Bang singularity with a smooth, nonsingular bounce driven by a repulsive curvature core proportional to a−6. A distinctive feature of the framework is the presence of a geometric slip term proportional to H˙, which encodes curvature-memory effects at the level of the background evolution without introducing additional propagating degrees of freedom. This term dynamically correlates the expansion rate with its temporal variation, leading to effective ultraviolet damping and enhanced dynamical stability across the high-curvature regime. As a consequence, the cosmological solutions admit the definition of an intrinsic relational time variable that is strictly monotonic throughout the evolution, including across the bounce. The emergent temporal ordering arises purely from geometric dynamics and does not rely on matter clocks, nonlocality, or fundamental violations of time-reversal or CPT symmetry. We discuss the consistency of the framework within its effective field theory domain of validity and comment on its implications for the conceptual problems of singularity resolution and the emergence of time in cosmology.

Quantum Reports doi: 10.3390/quantum8010019

Authors: Naveen Joy Sonet Daniel Thomas Aparna Rajan Lijin Varghese Aswathi Balakrishnan Amritha Thaikkad Vidya Niranjan Abhithaj Jayanandan Rajesh Raju

Accurate and early detection of bone cancer is critical for improving patient outcomes, yet conventional radiographic interpretation remains limited by subjectivity and variability. Conventional AI models often struggle with complex multi-modal noise distributions, non-convex and topologically entangled latent manifolds, extreme class imbalance in rare oncological conditions, and heterogeneous data fusion constraints. To address these challenges, we present a Quantum-Inspired Classical Convolutional Neural Network (QC-CNN) inspired by quantum analogies for automated bone cancer detection in radiographic images. The proposed architecture integrates classical convolutional layers for hierarchical feature extraction with a classical variational layer motivated by high-dimensional Hilbert space analogies for enhanced pattern discrimination. A curated and annotated dataset of bone X-ray images was utilized, partitioned into training, validation, and independent test cohorts. The QC-CNN was optimized using stochastic gradient descent (SGD) with adaptive learning rate scheduling, and regularization strategies were applied to mitigate overfitting. Quantitative evaluation demonstrated superior diagnostic performance, achieving high accuracy, precision, recall, F1-score, and area under the receiver operating characteristic curve (AUC). Results highlight the ability of classical CNN with quantum-inspired design to capture non-linear correlations and subtle radiographic biomarkers that classical CNNs may overlook. This study establishes QC-CNN as a promising framework for quantum-analogy motivated medical image analysis, providing evidence of its utility in oncology and underscoring its potential for translation into clinical decision-support systems for early bone cancer diagnosis. All computations in the present study are performed using classical algorithms, with quantum-inspired concepts serving as a conceptual framework for model design and motivating future extensions.

Quantum Reports doi: 10.3390/quantum8010018

Authors: Jussi Lindgren

The Stueckelberg wave equation is transformed into a quantum telegraph equation and a set of stationary states is obtained as unitary solutions. As it has been shown previously that this PDE relates to the Dirac operator, and on the other hand it is a linearized Hamilton–Jacobi–Bellman PDE, from which the Schrödinger equation can be deduced in a nonrelativistic limit, it is clear that it is the key equation in relativistic quantum mechanics. We give a Bayesian interpretation for the measurement problem. The stationary solution is understood as a maximum entropy prior distribution and measurement is understood as a Bayesian update. We discuss the interpretation of the single electron experiments in the light of finite speed propagation of the transition probability field and how it relates to the interpretation of quantum mechanics more broadly.

Quantum Reports doi: 10.3390/quantum8010017

Authors: Alka Verma Devanshi Katiyar Vimal Mishra Rajeev Gupta Yogendra Kumar Prajapati

The photonic spin Hall effect (PSHE) originates from the spin–orbit interaction (SOI) of light. The literature indicates that the transverse spin-dependent shift, δH− (SDS), from the PSHE is weak (in the nanometer range) and difficult to measure directly. This study utilizes a plasmonic structure to improve the δH− in the PSHE. The obtained results of this study demonstrate that the inclusion of silicon nitride (Si3N4) significantly enhances the δH− relative to its absence; however, plasmonic material is present in both cases. The enhanced shifts exhibit a significant dependence on the resonance angle (θr) and the thickness of layers of the PSHE structure to attain the maximum increase in δH− of 350.82 µm at the plasmonic resonance condition. A systematic analysis of the centroid positions of the reflected beam indicates a distinct and constant separation of opposing spin components. Further, the improved δH− is utilized in cancer cell detection, as changes in the refractive index (RI) of cells facilitate the identification of cancer cells from healthy to cancerous. All examined cell types demonstrate that cancerous cells had a greater δH− than normal cells, owing to their elevated effective RI. These results illustrate that the proposed plasmonic-assisted PSHE structure offers significant enhancement and a high sensitivity of 439.30 µm/RIU for label-free detection of cancer cells.

Quantum Reports doi: 10.3390/quantum8010016

Authors: Kees van Hee Kees van Berkel Jan de Graaf

The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This contradiction led many to question the underlying assumptions, viz. so-called realism and locality. The probability model underlying the Bell inequality is generally left implicit. We propose an explicit probability model for the CHSH version of the Bell experiment. This model has only two simultaneously observable detector settings per measurement, and therefore does not assume realism. The quantum expectation now becomes a conditional expectation, given the two detector settings. This probability model is in full agreement with both quantum mechanics and experiments. As a result, the model satisfies the Bell inequality; there are no so-called violations. We extend this model to include a hidden variable. This extended model is not Bell-separable. This non-separability implies that the model is non-deterministic or non-local (or both).

Quantum Reports doi: 10.3390/quantum8010015

Authors: Stefalo Acha

The Quantum Omni-Synthesis (QOS) framework is inspired by the cosmological constant problem, the dark sector, and the tension that arises when gravity is treated as purely geometrical while quantum fields remain defined on a fixed background. QOS adopts the working hypothesis that the dominant components of the dark sector correspond to two complementary energetic tendencies already familiar from known physics: confining, binding-dominated behavior and dispersive, propagating behavior. For clarity of interpretation, these are referred to as implosive and explosive energy, respectively. This terminology is not intended to redefine cosmological dark matter or dark energy, but to provide an effective language for tracking how different forms of energy contribute to localization, propagation, and gravitational coupling across scales. QOS postulates that every field configuration admits a decomposition of its local energy density into these two complementary components. A dimensionless scalar quantity, the Quantized Gravity Coupling Parameter ς(x), quantifies the local fraction of implosive energy. Spacetime curvature in QOS is generated primarily by the implosive fraction, while explosive energy contributes to propagation and vacuum activity without sourcing gravity at the same strength. In this paper, a field-theoretical realization of this idea is presented for a single real scalar field. A QOS-modified Lagrangian is introduced in which the kinetic term is weighted by a factor A(ψ,∇ψ)=1−ς2(ψ,∇ψ) that encodes the local balance between gradient and potential energy. From this Lagrangian, the nonlinear field equation and the corresponding energy momentum tensor are derived in full generality, including the effects of the functional dependence of A on the field and its derivatives. An effective Ricci tensor is constructed as Rμνeff=Rμν+fμν, where the correction fμν is expressed in terms of derivatives of Φ=ln(1−ς2) and arises from the energetic weighting rather than an independent scalar degree of freedom. The resulting QOS field equation couples this scalar sector to curvature without introducing a separate Brans–Dicke-like field.

Quantum Reports doi: 10.3390/quantum8010014

Authors: Boqun Song Jonathan D. H. Smith Jigang Wang

The position operator r^ appears as i∂p in wave mechanics, while its matrix form (e.g., under a Bloch basis) is well known diverging in diagonals, causing difficulties in basis transformation, observable yielding, etc. We aim to find a convergent r-matrix (CRM) to improve the existing divergent r-matrix (DRM), and investigate its influence at both the conceptual and the application levels. A key modification is increasing the familiar substitution of r^ by i∂p to i∑j∂kj, namely the N-th Weyl algebra. Resolving the divergence makes r-matrix rigorously defined, and we are able to show r-matrix is distinct from a spin matrix in terms of its defining principles, transformation behavior, and the observable it yields. Conceptually, the CRM fills the logical gap between the r-matrix and the Berry connection (this unremarked vagueness has caused the diagonal divergence). In application, we focus on transport, and discover that the Hermitian matrix is not identical with the associative Hermitian operator, i.e., rm,n=rn,m*⇎r^=r^†, which subtly affects the celebrated Berry curvature formula for adiabatic current. We also discuss how such a non-representation CRM can contribute to building a unified transport theory.

Quantum Reports doi: 10.3390/quantum8010013

Authors: Fernando C. Lombardo Paula I. Villar

We analyze the geometric phase and dynamic phase acquired by a qubit coupled to an environment through pure dephasing, establishing a direct connection between phase accumulation and ergotropy. We show that the dynamic phase depends solely on the incoherent ergotropy, reflecting its purely energetic origin. In contrast, the geometric phase exhibits a nontrivial dependence on both the coherent and incoherent contributions to the total ergotropy, encoding the interplay between coherence, dissipation, and energy extraction. By performing a perturbative expansion in the qubit–environment coupling strength, we demonstrate that, in the weak-coupling and long-time regime, the geometric phase becomes determined exclusively by the incoherent ergotropy, which coincides with the asymptotic value of the total ergotropy reached under decoherence. These results provide a clear physical distinction between dynamic and geometric phases in open quantum systems and establish geometric phases as sensitive probes of energetic resources. Furthermore, in superconducting circuit implementations, our findings suggest that the ergotropy of a two-level system could be inferred indirectly from geometric-phase measurements using standard techniques such as quantum state tomography.

Quantum Reports doi: 10.3390/quantum8010012

Authors: Riccardo Fantoni

We formulate a new quantum many-body simulation method for a general quantum fluid at any given temperature. Unlike the path integral Monte Carlo method, our method evolves, in imaginary time, the density matrix from its initial delta function condition to its final thermal form in an amount of time equal to the inverse temperature. It does this with a molecular dynamics scheme applied to a classical Hamiltonian that has the same functional form as the one for the quantum mechanical Hamiltonian according to the properties of the continuous representation of John R. Klauder. We then end up with the thermal density matrix, which can be used to extract thermal averages of observables using the Monte Carlo method equally well in any statistics.

Quantum Reports doi: 10.3390/quantum8010011

Authors: Jean-Christophe Pain

The purpose of this article is to highlight the connections between two seemingly distinct domains: random walks and the distribution of angular-momentum projections in quantum physics (the magnetic quantum numbers m). It is well known that there is indeed a deep mathematical link between the two, via the vector composition of angular momenta and rotational symmetry. Random walks are considered in the framework of an interpretation of the probability of microstates in statistical physics. The ideas presented in this work aim to illustrate the relevance of this perspective for modeling angular momentum in atomic physics.

Quantum Reports doi: 10.3390/quantum8010010

Authors: Takashi Kawakami Satoru Yamada Masateru Taniguchi Kizashi Yamaguchi

Electronic and spin structures of open-shell molecules and clusters were investigated as possible building blocks for the construction of one- and two-dimensional quantum spin alignment systems which exhibited several characteristic quantum properties of strongly correlated electron systems: high-Tc superconductivity, quantum spin coherence, entanglement, etc. Ab initio calculations were performed to elucidate effective exchange integrals (J) for 3d transition metal oxides, providing the J-model for high-Tc superconductivity. Theoretical investigations such as Monte Carlo simulation, molecular mechanics and quantum mechanical calculations were performed to elucidate effective chemical procedures for through-bond alignments of open-shell transition metal ions by organometallic conjugation and through-space confinements of molecular spins such as molecular oxygen by molecular confinement materials. Theoretical simulations have elucidated the importance of appropriate confinement materials for alignments of molecular spins desired for quantum coherence and quantum sensing. Equivalent transformations among coherent states of superconductors, trapped ion, neutral atom, molecular spin, molecular exciton, etc., are also discussed on theoretical and conceptual grounds such as quantum entanglement and decoherence.

Quantum Reports doi: 10.3390/quantum8010009

Authors: Shangkun Wang Chunle Ni

Quantum technology, a critical 21st-century strategic frontier science, has been a key technological competition between China and the U.S. This study employs natural language processing (NLP) techniques and a technology analytical framework to analyze the quantum technology policies of both countries. While the U.S. emphasized free-market innovation and global technological leadership on quantum technology from 2018 to 2024, China prioritized government-led development and socioeconomic stability. Moreover, the Chinese government adopts a systematic top-down approach characterized by government planning and direct intervention. However, the U.S. fosters innovation through market mechanisms and industry-academia collaboration. U.S. policies have gradually shifted from pure technological innovation to national security considerations. On the other hand, China has moved from breakthrough research to industrial deployment and application. These policy differences reflect distinct political systems and governance models, which may also resonate with their respective cultural traditions and philosophical foundations. Our findings fill a critical gap in comparative quantum technology policy research, offering significant insights for policymakers, researchers, and international stakeholders.

Quantum Reports doi: 10.3390/quantum8010008

Authors: Parker Emmerson (Yaohushuason)

Bell–CHSH is an inequality about unconditional expectations: under measurement independence, Bell locality, and bounded outcomes, the CHSH value satisfies S≤2. Experimental correlators, however, are often computed on an accepted subset of trials defined by detection logic, coincidence matching, quality cuts, and analysis windows. We model this by an acceptance probability γ(a,b,λ)∈[0,1] and the resulting accepted hidden-variable law νab obtained by weighting the measurement-independent prior ρ by γ and renormalizing. If νab depends on the setting pair then the four correlators entering CHSH are expectations under four different measures, and a Bell-local measurement-independent model can yield Sobs>2 by selection alone. We quantify the required setting dependence in total variation (TV) distance. For any reference law μ we prove the sharp bound Sobs≤2+2∑q∈QTV(νq,μ) for a CHSH quartet Q. Optimizing over μ yields the intrinsic dispersion bound Sobs≤2+2ΔQ, and, in particular, Sobs≤min{4,2+6DQ}, where DQ is the quartet TV diameter. The constants are optimal. Consequently, reproducing Tsirelson’s value 22 within Bell-local measurement-independent models via setting-dependent acceptance requires ΔQ≥2−1 (hence, DQ≥(2−1)/3). We then propose a two-lane experimental audit protocol: (i) prior-relative fair-sampling diagnostics using tags recorded on all trials, and (ii) prior-free dispersion diagnostics using accepted-tag distributions across settings, with ΔQ,X computable by linear programming on finite tag alphabets.

Quantum Reports doi: 10.3390/quantum8010007

Authors: Dayton C. Closser Zbigniew J. Kabala

What is the fastest Artificial Intelligence Large Language Model (AI LLM) for generating quantum operations? To answer this, we present the first benchmarking study comparing popular and publicly available AI models tasked with creating quantum gate designs. The Wolfram Mathematica framework was used to interface with the six AI LLMs, including Google Gemini 2.0 Flash, Anthropic Claude 3 Haiku, WolframLLM Notebook Assistant For Mathematica V14.3.0.0, OpenAI ChatGPT Omni 4 Mini, Google Gemma 3 4b 1t, and DeepSeek Chat V3. Our novel study found the following: (1) Gemini 2.0 Flash is overall the fastest AI LLM of the models tested in producing average quantum gate designs at 2.66101 s, factoring in the “thinking” execution time and ServiceConnect network latencies. (2) On average, four out of the ten quantum operations that the six LLMs produced compiled in Python version 3.13.5 (40.8% success rate). (3) Quantum operations averaged approximately 21–45 Lines of Code (omitting nonsensical outliers). (4) DeepSeek Chat V3 produced the shortest code with an average of 21.6 lines. This comparison evaluates the time taken by each AI LLM platform to generate quantum operations (including ServiceConnect networking times). These findings highlight a promising horizon where publicly available Large Language Models can become fast collaborators with quantum computers, enabling rapid quantum gate synthesis and paving the way for greater interoperability between two remarkable and cutting-edge technologies.

Quantum Reports doi: 10.3390/quantum8010006

Authors: Na Hai Zijian Liu Bowen Zhang Tingyu Li Xiuqing Yang Zhenghong Li

Counterfactual quantum control is a novel control method, in which no actual material particles or energy are transported and exchanged between the controller and the controlled. By introducing the quantum Zeno effect where the evolution of a quantum system can be suppressed by continuous observation, this paper presents a review of research progress in counterfactual quantum control. The basic concept of counterfactual quantum control is presented and macro counterfactual quantum control is thoroughly discussed. In addition, related experimental verification and applied exploration are also discussed. This review paper covers the progress toward counterfactual quantum communication, non-invasive imaging and specific applications.

Quantum Reports doi: 10.3390/quantum8010005

Authors: John T. Solomon

Conventional quantum mechanics treats the electron as a point-like particle endowed with intrinsic properties—mass, charge, and spin—that are inserted as axioms rather than derived from first principles. Here, we propose a thermodynamic reformulation of the electron grounded in entropy field dynamics, based on S-Theory. In this framework, the electron is composed of three distinct entropic components: Score (a collapsed entropy core from configurational mass), SEM (a structured electromagnetic entropy field from charge), and Sthermal (a diffuse entropy component from ambient interactions). We show that spin emerges as a rotating SEM shell around Score, and that electron collapse—as in quantum measurement—can be modeled as a Recursive Amplification of Sfield (RAS) process driven by entropic feedback. Through mathematical formulation and high-resolution simulations, we demonstrate how the S-field components evolve under entropic excitation, culminating in a collapse threshold defined by local entropy density matching. This model not only explains the emergence of quantum properties but also offers a thermodynamic mechanism for electron–photon interaction, wavefunction collapse, and spin generation, revealing the inner structure and dynamics of one of nature’s most fundamental particles.

Quantum Reports doi: 10.3390/quantum8010004

Authors: Gastón Sanglier Contreras Roberto Alonso González-Lezcano Eduardo J. López Fernández

We propose a unified theoretical framework grounded in a Primordial Quantum Field (PQF)—a continuous, non-local informational substrate that precedes space-time and matter. The PQF is represented by a wave functional evolving in an abstract configuration space, where physical properties emerge through the self-organization of complexity. We introduce a novel physical quantity—complexity entropy Sc[ϕ]—which quantifies the structural organization of the PQF. Unlike traditional entropy measures (Shannon, von Neumann, Kolmogorov), Sc[ϕ] captures non-trivial coherence and functional correlations. We demonstrate how complexity gradients induce an emergent geometry, from which spacetime curvature, physical constants, and the arrow of time arise. The model predicts measurable phenomena such as entanglement waves and reinterprets dark energy as informational coherence pressure, suggesting empirical pathways for testing via highly correlated quantum systems.

Quantum Reports doi: 10.3390/quantum8010003

Authors: Andrei T. Patrascu

Quantum anomalies are traditionally understood as classical symmetries that fail to survive quantization, while experimental “anomalies” denote deviations between theoretical predictions and measured values. In this work, we develop a unified framework in which both phenomena can be interpreted through the lens of algebraic quantum field theory (AQFT). Building on the renormalization group viewed as an extension problem, we show that renormalization ambiguities correspond to nontrivial elements of Hochschild cohomology, giving rise to a deformation of the observable algebra A∗B=AB+εω(A,B), where ω is a Hochschild 2-cocycle. We interpret ω as an intrinsic algebraic curvature of the net of local algebras, namely the (local) Hochschild class that measures the obstruction to trivializing infinitesimal scheme changes by inner redefinitions under locality and covariance constraints. The transported product is associative; its first-order expansion is associative up to O(ε2) while preserving the ∗-structure and Ward identities to the first order. We prove the existence of nontrivial cocycles in the perturbative AQFT setting, derive the conditions under which the deformed product respects positivity and locality, and establish the compatibility with current conservation. The construction provides a direct algebraic bridge to standard cohomological anomalies (chiral, trace, and gravitational) and yields correlated deformations of physical amplitudes. Fixing the small deformation parameter ε from the muon (g−2) discrepancy, we propagate the framework to predictions for the electron (g−2), charged lepton EDMs, and other low-energy observables. This approach reduces reliance on ad hoc form-factor parametrizations by organizing first-order scheme-induced deformations into correlation laws among low-energy observables. We argue that interpreting quantum anomalies as manifestations of algebraic curvature opens a pathway to a unified, testable account of renormalization ambiguities and their phenomenological consequences. We emphasize that the framework does not eliminate renormalization or quantum anomalies; rather, it repackages the finite renormalization freedom of pAQFT into cohomological data and relates it functorially to standard anomaly classes.

Quantum Reports doi: 10.3390/quantum8010002

Authors: Bin Li

We revisit the premise that spacetime geometry must be quantized and show that this assumption is not physically required. Just as one does not quantize pressure or temperature, quantizing the metric treats a macroscopic continuum variable as if it were microscopic. We develop an alternative approach, Chronon Field Theory (ChFT), in which a smooth timelike covector Φμ obeys a unified variational principle—the Temporal Coherence Principle (TCP). In appropriate long-wavelength and low-vorticity regimes, the TCP dynamics yield an emergent Lorentzian metric and reproduce the Einstein field equations to leading order. Phase-coherent excitations exhibit a universal invariant speed and admit an eikonal limit that reproduces Hamilton–Jacobi and Schrödinger-type dynamics. Despite the presence of a microscopic causal alignment field, exact operational Lorentz invariance is preserved because all observers and measuring devices co-emerge from the same causal medium. The framework predicts small higher-order dispersive corrections to relativistic propagation while maintaining a universal causal cone, with effects constrained by fast radio burst and multi-messenger observations. ChFT thus provides a compact effective description in which gravitational and quantum dynamics emerge from a single coherence principle, without postulating quantum geometry at the fundamental level.

Quantum Reports doi: 10.3390/quantum8010001

Authors: Mehrzad Soltani Mark J. Balas

Time evolution of open quantum systems is governed by the master equation. The master equation, which is a matrix formalism, is the time derivative of the density matrix, which contains the complete information on the state of a quantum system. Instead of implementing successive measurements on repeated identically prepared systems, which are inevitably imperfect and can only be performed a limited number of times, a state estimator can be designed to obtain the whole information about the state of a quantum system represented in a density matrix. Trace-one and positive semi-definite properties of the density matrix arising from physical constraints have to be preserved during state estimation in quantum systems. To address this challenge, we present a projection technique that incorporates Dykstra’s algorithm and physical constraints into state estimation. This technique, which is an iterative method, ensures convergence and includes a designed oracle that projects the estimated state into intersections of admissible closed convex sets. The oracle structure is constructed using Hilbert projection, which looks for the best approximation of the projected estimated state within a Hilbert space into a closed convex set. According to the Hilbert projection theorem, this proposed oracle guarantees the existence and uniqueness of the best approximation of the projected state.

Quantum Reports doi: 10.3390/quantum7040064

Authors: Satinder Singh Avnish Thakur Moin Hasan Guneet Singh Bhatia

Face recognition systems are widely used for biometric authentication but face two major problems. First, processing high-resolution images and large databases requires extensive computational time. Second, emerging quantum computers threaten to break the encryption methods that protect stored facial templates. Quantum computers will soon be able to decrypt current security systems, putting biometric data at permanent risk since facial features cannot be changed like passwords. This paper presents a solution that uses quantum computing to speed up face recognition while adding quantum-resistant security. It applies quantum principal component analysis (QPCA) and the SWAP test to reduce the computational complexity and implement lattice-based cryptography, which quantum computers cannot break. Experimental evaluation demonstrates a significant overall speedup with improved accuracy. The proposed framework achieves a significant improvement in performance, provides 125-bit security against quantum attacks and compresses the data storage requirements significantly. These results demonstrate that quantum-enhanced face recognition can solve both the speed and security challenges facing current biometric systems, making it practical for real-world deployment as quantum technology advances.

Quantum Reports doi: 10.3390/quantum7040063

Authors: Yassine Chargui Sultan Al-Harbi

We derive the exact eigenfunctions and energy equation for a Dirac particle in a monochromatic quantized electromagnetic plane wave and a confining scalar linear potential. It is shown that the system’s energy spectrum exhibits a forbidden region that vanishes when the particle–field interaction is switched off. We then analyze the effect of particle–field coupling on quantum entanglement between the particle’s spin and the remaining degrees of freedom. Our results show that the profile of the spin–rest entanglement, measured by negativity and Von Neumann entropy, follows the energy profile of the state: it is monotonic when the energy is monotonic, and non-monotonic otherwise. These results may provide insights into quantum correlations in Dirac-like systems describing low-energy excitations of graphene and trapped ions.

Quantum Reports doi: 10.3390/quantum7040062

Authors: Ghenadie N. Mardari

The concept of correlation appears straightforward: measurement outcomes coincide, and patterns emerge. For any record of events, the coefficients are uniquely determined. Thus, if correlations change spontaneously, as seen in quantum monogamy, then individual behavior must have changed first. Surprisingly, this is not always true. When two observables are mutually exclusive, they cannot coincide objectively and need to be grouped across time. Yet, sectioning the flow of events into “iterations” is not trivial in this case. Even with blind windows of coincidence, the same order of outcomes can produce different coefficients of correlation, depending on the number of joint measurements. Therefore, quantum monogamy can happen with fixed pre-determined events. A new concept (“subjective correlation”) is required to explain this phenomenon.

Quantum Reports doi: 10.3390/quantum7040061

Authors: Bin Li

Quantum mechanics postulates wave–particle duality and assigns amplitudes of the form eiS/ℏ, yet no existing formulation explains why physical observables depend only on the phase of the action. Here we show that if the quantum of action ℏgeom is finite, the classical action manifold R becomes compact under the identification S≡S+2πℏgeom, yielding a U(1) action space on which only modular action is observable. Wave interference then follows as a geometric necessity: a finite action quantum forces physical amplitudes to live on a circle, while the classical limit arises when the modular spacing 2πℏgeom becomes negligible compared with macroscopic actions. We formulate this as a compact-action theorem. Chronon Field Theory (ChFT) provides the physical origin of ℏgeom: its causal field Φμ carries a quantized symplectic flux ∮ω=ℏgeom, making Planck’s constant a geometric topological invariant rather than an imposed parameter. Within this medium, the Real–Now–Front (RNF) supplies a local reconstruction rule that reproduces the structure of the Feynman path integral, the Schrödinger evolution, the Born rule, and macroscopic definiteness as consequences of geometric compatibility rather than supplemental postulates. Phenomenologically, identifying the electron as the minimal chronon soliton—carrying the fundamental unit of symplectic flux—links its spin, charge, and stability to topological properties of the chronon field, yielding concrete experimental signatures. Thus the compact-action/RNF framework provides a unified geometric origin for quantum interference, measurement, and matter, together with falsifiable predictions of ChFT.

Quantum Reports doi: 10.3390/quantum7040060

Authors: Zdzislaw E. Musielak

Theories of modern physics are based on dynamical equations that describe the evolution of particles and waves in space and time. In classical physics, particles and waves are described by different equations, but this distinction disappears in quantum physics, which is predominantly based on wave-like equations. The main purpose of this paper is to present a comprehensive review of all known classical and quantum linear wave equations for scalar wavefunctions, and to discuss their origin and applications to a broad range of physical problems.

Quantum Reports doi: 10.3390/quantum7040059

Authors: Wei Wen

The Feynman path integral plays a central role in quantum mechanics, linking classical action to propagators and relating quantum electrodynamics (QED) to Feynman diagrams. However, the path-integral formulations used in non-relativistic quantum mechanics and in QED are neither unified nor directly connected. This suggests the existence of a missing path integral that bridges relativistic action and the Dirac equation at the single-particle level. In this work, we analyze the consistency and completeness of existing path-integral theories and identify a spinor path integral that fills this gap. Starting from a relativistic action written in spinor form, we construct a spacetime path integral whose kernel reproduces the Dirac Hamiltonian. The resulting formulation provides a direct link between the relativistic classical action and the Dirac equation, and it naturally extends the scalar relativistic path integral developed in our earlier work. Beyond establishing this structural connection, the spinor path integral offers a new way to interpret the origin of classical mechanics for the Dirac equation and suggests a spacetime mechanism for spin and quantum nonlocal correlations. These features indicate that the spinor path integral can serve as a unifying framework for existing path-integral approaches and as a starting point for further investigations into the spacetime structure of quantum mechanics.

Quantum Reports doi: 10.3390/quantum7040058

Authors: Majid Monajjemi Fatemeh Mollaamin

The anion, cation, and radical structural forms of B2N (−,0,+) were studied in the case of symmetry breaking (SB) inside a (5, 5) BN nanotube ring and were also compared in terms of non-covalent interaction between these two parts. The non-bonded system of B2N (−,0,+) and the (5, 5) BN nanotube not only causes SB for BNB but also creates an energy barrier in the range of 10−3 Hartree of due to this non-bonded interaction. Moreover, several SBs appear via asymmetry stretching and symmetry bending normal mode interactions according to the multiple second-order Jahn–Teller effect. We also demonstrated that the twin minimum of BNB’s potential curve arises from the lack of a proper wave function with permutation symmetry, as well as abnormal charge distribution. Through this investigation, considerable enhancements in the energy barriers due to the SB effect were also observed during the electrostatic interaction of BNB (both radical and cation) with the BN nanotube ring. Additionally, these values were not observed for the isolated B2N (−,0,+) forms. This non-bonded complex operates as a quantum rotatory model and as a catalyst for producing a range of spectra in the IR region due to the alternative attraction and repulsion forces.

Quantum Reports doi: 10.3390/quantum7040057

Authors: Christopher S. Jackson

Many of the most fundamental observables—position, momentum, phase point, and spin direction—cannot be measured by an instrument that obeys the orthogonal projection postulate. Continuous-in-time measurements provide the missing theoretical framework to make physical sense of such observables. The elements of the time-dependent instrument define a group called the instrumental group (IG). Relative to the IG, all of the time dependence is contained in a certain function called the Kraus-operator density (KOD), which evolves according to a classical Kolmogorov equation. Unlike the Lindblad master equation, the KOD Kolmogorov equation is a direct expression of how the elements of the instrument (not just the total quantum channel) evolve. Shifting from continuous measurements to sequential measurements more generally, the structure of combining instruments in sequence is shown to correspond to the convolution of their KODs. This convolution promotes the IG to an involutive Banach algebra (a structure that goes all the way back to the origins of POVM and C*-algebra theory), which will be called the instrumental group algebra (IGA). The IGA is the true home of the KOD, similar to how the dual of a von Neumann algebra is the true home of the density operator. Operators on the IGA, which play the analogous role for KODs as superoperators play for density operators, are called ultraoperators and various important examples are discussed. Certain ultraoperator–superoperator intertwining relationships are also considered throughout, including the relationship between the KOD Kolmogorov equation and the Lindblad master equation. The IGA is also shown to have actually two distinct involutions: one respected by the convolution ultraoperators and the other by the quantum channel superoperators. Finally, the KOD Kolmogorov generators are derived for jump processes and more general diffusive processes.

Quantum Reports doi: 10.3390/quantum7040056

Authors: Samaneh Bagheri Novir

Quantum computers, due to their superposition and entanglement properties, provide significant advantages in solving certain problems compared with classical computers. Therefore, it is crucial to identify issues that can be efficiently solved by noisy intermediate-scale quantum (NISQ) systems. Xanadu has introduced the X8 quantum chip, based on integrated photonic technology, along with important photonic platforms such as Strawberry Fields and Gaussian Boson Sampling (GBS), to solve specific computational problems. In this review article, after reviewing Boson Sampling (BS) and Gaussian Boson Sampling (GBS), we discuss the relationship between GBS and graph theory, including how graphs can be encoded in GBS. Some applications of GBS, particularly molecular docking and molecular vibrations, are also considered. The future goal of this study is to identify problems that can be represented as small graphs and solved using GBS with a limited number of optical modes.

Quantum Reports doi: 10.3390/quantum7040055

Authors: Johan Heriberto Rúa Muñoz Jorge Eduardo Mahecha Gómez Santiago Pineda Montoya

We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation over H is polynomially equivalent to the standard complex quantum circuit model and hence captures the same complexity class BQP up to polynomial reductions. Over H, we construct a complete model—quaternionic qubits on right H-modules with quaternion-valued inner products, unitary dynamics, associative tensor products, and universal gate sets—and establish polynomial equivalence with the standard complex model; routes for implementation at fidelities exceeding 99% via pulse-level synthesis on current hardware are discussed. Over O, non-associativity yields path-dependent evolution, ambiguous adjoints/inner products, non-associative tensor products, and possible failure of energy conservation outside associative sectors. We formalize these obstructions and systematize four mitigation strategies: Confinement to associative subalgebras, G2-invariant codes, dynamical decoupling of associator terms, and a seven-factor algebraic decomposition for gate synthesis. The results delineate the feasible quaternionic regime from the constrained octonionic landscape and point to applications in symmetry-protected architectures, algebra-aware simulation, and hypercomplex learning.

Quantum Reports doi: 10.3390/quantum7040054

Authors: Nicos Makris

In view of the remarkable progress in microrheology to monitor the random motion of Brownian particles with a size as small as a few nanometers, and given that de Broglie matter waves have been experimentally observed for large molecules of comparable nanometer size, we examine whether Brownian particles can manifest a particle-wave duality without employing a priori arguments from quantum decoherence. First, we examine the case where Brownian particles are immersed in a memoryless viscous fluid with a time-independent diffusion coefficient, and the requirement for the Brownian particles to manifest a particle-wave duality leads to the untenable result that the diffusion coefficient has to be proportional to the inverse time, therefore, diverging at early times. This finding agrees with past conclusions published in the literature, that quantum mechanics is not equivalent to a Markovian diffusion process. Next, we examine the case where the Brownian particle is trapped in a harmonic potential well with and without dissipation. Both solutions of the Fokker–Planck equation for the case with dissipation, and of the Schrödinger equation for the case without dissipation, lead to the same physically acceptable result—that for the Brownian particle to manifest a particle-wave duality, its mean kinetic energy kBT/2 needs to be ½ the ground-state energy, E0=12ℏω of the quantum harmonic oscillator. Our one-dimensional calculations show that for this to happen, the trapping needs to be very strong so that a Brownian particle with mass m and radius R needs to be embedded in an extremely stiff solid with shear modulus, G proportional to m/RkBT/ℏ2.

Quantum Reports doi: 10.3390/quantum7040053

Authors: Ali Shojaei-Fard

The mathematical universe of the quantum topos, which is formulated on the basis of classical Boolean snapshots, delivers a neo-realist description of quantum mechanics that preserves realism. The main contribution of this article is developing formal objectivity in physical theories beyond quantum mechanics in the topos-theory approach. It will be shown that neo-realist responses to non-perturbative structures of quantum field theory do not preserve realism. In this regard, the method of Feynman graphons is applied to reframe the task of describing objectivity in quantum field theory in terms of replacing the standard Hilbert-space/operator-algebra ontology with a new context category built from a certain family of topological Hopf subalgebras of the topological Hopf algebra of renormalization as algebraic/combinatorial data tied to non-perturbative structures. This topological-Hopf-algebra ontology, which is independent of instrumentalist probabilities, enables us to reconstruct gauge field theories on the basis of the mathematical universe of the non-perturbative topos. The non-Boolean logic of the non-perturbative topos cannot be recovered by classical Boolean snapshots, which is in contrast to the quantum-topos reformulation of quantum mechanics. The article formulates a universal version of the non-perturbative topos to show that quantum field theory is a globally and locally neo-realist theory which can be reconstructed independent of the standard Hilbert-space/operator-algebra ontology. Formal objectivity of the universal non-perturbative topos offers a new route to build objective semantics for non-perturbative structures.

Quantum Reports doi: 10.3390/quantum7040052

Authors: Massimo E. Maffei

The Earth’s geomagnetic field (GMF) is a fundamental environmental signal for plants, with its perception rooted in quantum biology. Specifically, the radical pair mechanism (RPM) explains how this weak force influences electron spin states in metabolic pathways, providing a framework for its profound biological impact. Research shows that a hypomagnetic field (hMF) directly reduces the production of reactive oxygen species (ROS), creating a quantum signature in plants. This is a counterintuitive finding, as it suggests the plant perceives less oxidative stress and, in response, downregulates its antioxidant defenses. This multi-level effect, from a quantum trigger to molecular and metabolic changes, ultimately affects the plant’s growth and phenotype. This review suggests a possible link between the GMF and plant health, identifying the GMF as a potential physiological modulator. Manipulating the magnetic field could therefore be a novel strategy for improving crop resilience and growth. However, the fact that some effects cannot be fully explained by the RPM suggests other quantum mechanisms are involved, paving the way for future research into these undiscovered processes and their potential inheritance across generations.

Quantum Reports doi: 10.3390/quantum7040051

Authors: Grégoire Cattan Anton Andreev Quentin Barthélemy

The nearest convex hull (NCH) classifier is a promising algorithm for the classification of biosignals, such as electroencephalography (EEG) signals, especially when adapted to the classification of symmetric positive definite matrices. In this paper, we implemented a version of this classifier that can execute either on a traditional computer or a quantum simulator, and we tested it against state-of-the-art classifiers for EEG classification. This article addresses the practical challenges of adapting a classical algorithm to one that can be executed on a quantum computer or a quantum simulator. One of these challenges is to find a formulation of the classification problem that is quadratic, is binary, and accepts only linear constraints—that is, an objective function that can be solved using a variational quantum algorithm. In this article, we present two approaches to solve this problem, both compatible with continuous variables. Finally, we evaluated, for the first time, the performance of the NCH classifier on real EEG data using both quantum and classical optimization methods. We selected a particularly challenging dataset, where classical optimization typically performs poorly, and demonstrated that the nearest convex hull classifier was able to generalize with a modest performance. One lesson from this case study is that, by separating the objective function from the solver, it becomes possible to allow an existing classical algorithm to run on a quantum computer, as long as an appropriate objective function—quadratic and binary—can be found.

Quantum Reports doi: 10.3390/quantum7040050

Authors: Jiaqiang Zhao Haoxiang Qin Lianzhen Cao Yang Yang Xia Liu Qinwei Zhang Huaixin Lu Kellie Ann Driscoll Meijiao Wang

Due to the important role of quantum information technology in the future development of science and technology, researchers have extensively studied the preparation, characterization, and application of quantum systems. It is of great significance to further study the universality and generalization of multi-qubit entangled states. Especially in quantum communication, the actual quantum system is always affected by various noises from the environment. Noise has a significant impact on the properties of the actual quantum system, so we study the effects of noise on a prepared two-photon four-qubit state by two methods. We experimentally simulated the most common bit-flip noise in quantum systems. The law of evolution of the fidelity of two-dimensional four-qubit states and violation of the Mermin inequality and the Ardehali inequality for LR under different levels of bit-flip noise are investigated. The experimental results show that entanglement fidelity and nonlocality can be used to judge the degree of noise interference in the quantum channel and, thus, judge the security of the quantum communication channel. This judgment is of great significance for the realization of practical long-distance multi-node quantum communication.

Quantum Reports doi: 10.3390/quantum7040049

Authors: Michel Planat

By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z5⋊2I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its SL(2,C) character variety yields elliptic curves whose L-function derivatives L′(E,1) remarkably match fundamental biological structural ratios. Specifically, we demonstrate that the Birch–Swinnerton-Dyer conjecture’s central quantity: the derivative L′(E,1) of the L-function at 1 encodes critical cellular geometries: the crystalline B-DNA pitch-to-diameter ratio (L′(E,1)=1.730 matching 34Å/20Å=1.70), the B-DNA pitch to major groove width (L′=1.58) and, additionally, the fundamental cytoskeletal scaling relationship where L′(E,1)=3.570≈25/7, precisely matching the microtubule-to-actin diameter ratio. This pattern extends across the hierarchy Z5⋊2P with 2P∈{2O,2T,2I} (binary octahedral, tetrahedral, icosahedral groups), where character tables of 2O explain genetic code degeneracies while 2T yields microtubule ratios. The convergence of multiple independent mathematical pathways on identical biological values suggests that evolutionary optimization operates under deep arithmetic-geometric constraints encoded in elliptic curve L-functions. Our results position the BSD conjecture not merely as abstract number theory, but as encoding fundamental organizational principles governing cellular architecture. The correspondence reveals arithmetic geometry as the mathematical blueprint underlying major biological structural systems, with Gross–Zagier theory providing the theoretical framework connecting quantum topology to the helical geometries that are essential for life.

Quantum Reports doi: 10.3390/quantum7040048

Authors: Angelo Plastino Victoria Vampa

Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In this work, we provide what is, to our knowledge, the first explicit realization of the epistemic-to-physical transition of Fisher information within a finite interacting quantum system. Specifically, we analyze a model of N fermions occupying two degenerate levels and coupled by a spin-flip interaction of strength V, treated in the grand canonical ensemble at inverse temperature β. We compute the Fisher information FN(V) associated with the sensitivity of the thermal state to changes in V, and show that it becomes an observer-independent, experimentally meaningful quantity: it encodes fluctuations, tracks entropy variations, and reveals structural transitions induced by interactions. Our findings thus demonstrate that Fisher information, originally conceived as an inferential and epistemic measure, can operate as a bona fide thermodynamic observable in quantum many-body physics, bridging the gap between information-theoretic foundations and measurable physical law.

Quantum Reports doi: 10.3390/quantum7040047

Authors: Boris Arseniev Igor Zacharov

The simulation of multidimensional wave propagation with variable material parameters is a computationally intensive task, with applications from seismology to electromagnetics. While quantum computers offer a promising path forward, their algorithms are often analyzed in the abstract oracle model, which can mask the high gate-level complexity of implementing those oracles. We present a framework for constructing a quantum algorithm for the multidimensional wave equation with a variable speed profile. The core of our method is a decomposition of the system Hamiltonian into sets of mutually commuting Pauli strings, paired with a dedicated diagonalization procedure that uses Clifford gates to minimize simulation cost. Within this framework, we derive explicit bounds on the number of quantum gates required for Trotter–Suzuki-based simulation. Our analysis reveals significant computational savings for structured block-model speed profiles compared to general cases. Numerical experiments in three dimensions confirm the practical viability and performance of our approach. Beyond providing a concrete, gate-level algorithm for an important class of wave problems, the techniques introduced here for Hamiltonian decomposition and diagonalization enrich the general toolbox of quantum simulation.

Quantum Reports doi: 10.3390/quantum7040046

Authors: James Camparo

Over the past several decades, there has been an accelerating trend to ever more accurate quantum sensors: sensors of time intervals (i.e., atomic clocks), sensors of magnetic fields (i.e., quantum magnetometers), and sensors of inertial motions (i.e., atom interferometers), to name just a few. With this trend has come a renewed interest in the problem of quantum mechanical measurement (i.e., collapse of the wavefunction), and though there have been many attempts to resolve the problem, there is still no wholly accepted resolution. Here, we discuss a little-explored path for resolving the issue that exploits wavefunction phase. To illustrate this path’s potential, we consider the notion of “eigenphase” sets that are disjoint among orthogonal eigenvectors. Wavefunction collapse then occurs because of constructive/destructive interference when a classical measuring device “phase-locks” to an incoming wavefunction. While the present work examines one method for exploiting wavefunction phase, its primary purpose is to more generally re-focus attention on wavefunction phase as a means for resolving the measurement problem that avoids many other solutions’ problematic aspects.

Quantum Reports doi: 10.3390/quantum7040045

Authors: Justin P. Bergfield

Molecules provide the smallest possible circuits in which quantum interference and electron correlation can be engineered to perform logical operations, including the universal NAND gate. We investigate a chemically encoded quantum NAND tree based on alkynyl-extended iso-polyacetylene backbones, where inputs are set by end-group substitution and outputs are read from the presence or absence of transmission nodes. Using quantum many-body transport theory, we show that NAND behavior persists in the presence of dynamic correlations, but that the nodal positions and their chemical shifts depend sensitively on electron–electron interactions. This sensitivity highlights the potential of these systems not only to probe the strength of electronic correlations but also to harness them in shaping logical response. The thermopower is identified as a chemically robust readout of gate logic, providing discrimination margins that greatly exceed typical experimental uncertainties, in an observable governed primarily by the variation of transport rather than its absolute magnitude.

Quantum Reports doi: 10.3390/quantum7040044

Authors: Shatha Alhazmi Khaled Elleithy Abdelrahman Elleithy

As quantum computing advances, traditional digital forensic techniques face significant risks due to the vulnerability of classical cryptographic algorithms to quantum attacks. This review explores the emerging field of quantum digital forensics, with a particular focus on the role of quantum entanglement in enhancing the integrity, authenticity, and confidentiality of digital evidence. It compares classical and quantum forensic mechanisms, examines entanglement-based quantum key distribution (QKD), quantum hash functions, and quantum digital signatures (QDS), and discusses the challenges in practical implementation, such as scalability, hardware limitations, and legal admissibility. The paper also reviews various entanglement detection methods critical to the validation of quantum states used in forensic processes.

Quantum Reports doi: 10.3390/quantum7030043

Authors: Akihiro Nishiyama Shigenori Tanaka Jack Adam Tuszynski

This paper aims to address the possibility of parametric resonance effects in microtubules via tryptophan qubits, using the Hamiltonian of the cavity quantum electrodynamics (QED) model involving photons in a waveguide and the surrounding environment. The time evolution equations for qubits and photons are derived using the input–output formulation. Input signals with a 560 nm wavelength are amplified by Rabi oscillations for tryptophan qubits in excited states. Here, the qubits organized in multiple layers are all in excited states. When an appropriate decay to the environment occurs as internal loss, which is prepared in multiple layers, we find binary patterns of the parametric amplification of input signals and the reduction of output signals. This property might help us to understand the information processing of optical signals by filtering them with the use of tryptophan residues in microtubules and diffused nonlocal processing spreading over the whole brain in the form of holograms.

Quantum Reports doi: 10.3390/quantum7030042

Authors: Horace T. Crogman To Dang Daniel Erenso

We present a topologically protected teleportation protocol based on projective parity measurements between spatially separated Majorana zero modes (MZMs), eliminating the need for dynamic braiding. Unlike conventional teleportation schemes, our method preserves logical information through nonlocal encoding and suppresses decoherence exponentially with Majorana separation. We provide a rigorous mathematical framework that includes six theorems and a lemma, proving fidelity bounds, no entropy increase under ideal QND parity measurement under quantum non-demolition (QND) measurements, and compliance with the no-cloning theorem. We demonstrate that all correction operations lie within the Clifford group, enabling efficient, fault-tolerant implementation. Furthermore, we outline a scalable architecture for multi-qubit teleportation and relate our framework to recent experimental advances in quantum-dot-based Kitaev chains and superconducting nanowire platforms. These results position Majorana-based teleportation as a thermodynamically stable and experimentally viable approach to scalable quantum information transfer. All operations discussed are Clifford-only; achieving universality requires non-Clifford resources and lies outside our scope.

Quantum Reports doi: 10.3390/quantum7030041

Authors: Gilberto Díaz Luiz Steffenel Carlos Barrios Jean Couturier

Software quantum simulators are essential tools for designing and testing quantum algorithms on classical computing architectures, especially given the current limitations of physical quantum hardware. This work focuses on studying and evaluating memory management strategies for scalable quantum state simulation. We examine full-state representation, dynamic state pruning, shared-memory parallelization with OpenMP, distributed memory execution using MPI, and error-bounded floating-point compression with ZFP. These techniques are implemented in a prototype simulator and assessed using the quantum Fourier transform as a benchmark, with performance compared against leading open-source simulators such as Intel-QS, QuEST, and qsim. The results show the trade-offs between computational overhead and memory efficiency, and demonstrate that hybrid approaches combining distributed memory and compression can significantly extend the number of qubits that can be simulated. This work contributes practical insights for improving the scalability of software quantum simulators on classical hardware through optimized memory usage.

Quantum Reports doi: 10.3390/quantum7030040

Authors: Chiara Marletto Vlatko Vedral

We formally represent the quantum interference of a single qubit embodied by a photon in the Mach–Zehnder interferometer using the classical Hamiltonian framework but with complex canonical variables. Although all operations on a single qubit can be formally expressed using complex classical Hamiltonian dynamics, we show that the resulting system is still not a proper qubit. The reason for this is that it is not capable of getting entangled to another bona fide qubit and hence it does not have the information-processing capacity of a fully-fledged quantum system. This simple example powerfully illustrates the difficulties faced by hybrid quantum–classical models in accounting for the full range of behaviour of quantum systems.