Quantum Rep., Volume 8, Issue 3 (September 2026) – 19 articles

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. Full article

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. Full article

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 $R_{min}$, 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 $R_{min}$ 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 $d=4^6=4096$ 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 $27\times$ to $68\times$ 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. Full article

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. Full article

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/(8σ_x²) + σ_x²Δp²/(2ℏ²) is a quadratic phase-space distinguishability parameter that combines relative position and momentum displacements. The Gaussian entropy can therefore be written as S_s(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. Full article

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. Full article

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. Full article

Three results. (1) We prove the tensor-level conformal identity $d{s}_{\mathrm{BK}}^2=4{\gamma }^2\left(r\right) d{s}_{\mathrm{Bures}}^2$ between the Bures metric and the Beltrami–Klein metric on the open qubit Bloch ball, where ${\gamma }^2\left(r\right)=1/(1-r^2)$ 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 $I\left(V\right)=1/(1-V^2)={\gamma }^2\left(V\right)$. (3) The conformal structure is special to qubits; for $N\ge 3$, 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family $\left\{F_k\right\}$ is defined by $F_k\left(q\right)=\nabla S_k\left(q\right)$, the gradient of the generating function of a secret Lagrangian submanifold $L_k$ on the symplectic torus ${\mathbb{T}}^{2n}$. 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: $F_k$ is smooth ($C^{\infty }$), 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 ${\widehat{U}}_K^r$ 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 ${\widehat{U}}_K^r$. 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. Full article

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. Full article

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. Full article

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. Full article

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. Full article