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Volume 8
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Quantum Rep., Volume 8, Issue 2 (June 2026) – 19 articles

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44 pages, 13353 KB  
Article
A Hybrid Quantum-Classical Framework for Saliency-Aware Medical Image Encoding
by Vrushali Nikam, Trupti Atre, Lavanya Santhosh, Asha K N and Praveena M V
Quantum Rep. 2026, 8(2), 46; https://doi.org/10.3390/quantum8020046 - 7 May 2026
Viewed by 151
Abstract
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. [...] Read more.
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. Full article
(This article belongs to the Section Quantum Computing and Information Processing)
17 pages, 649 KB  
Article
A Two-Step Quantum Approximate Optimization Algorithm for Portfolio Optimization and Risk Assessment
by Boxuan Wu and Lei Wang
Quantum Rep. 2026, 8(2), 45; https://doi.org/10.3390/quantum8020045 - 7 May 2026
Viewed by 361
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Topic Quantum Systems and Their Applications)
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19 pages, 323 KB  
Article
Breakdown of Bell Factorization from Non-Injective Effective Descriptions
by Jérôme Beau
Quantum Rep. 2026, 8(2), 44; https://doi.org/10.3390/quantum8020044 - 2 May 2026
Viewed by 312
Abstract
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 [...] Read more.
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. Full article
13 pages, 456 KB  
Article
Noise Mitigation in Quantum-Enhanced Fiber Optic Gyroscopes
by Stefan Evans and Joanna N. Ptasinski
Quantum Rep. 2026, 8(2), 43; https://doi.org/10.3390/quantum8020043 - 1 May 2026
Viewed by 244
Abstract
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 [...] Read more.
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. Full article
18 pages, 394 KB  
Article
Many Body in General Relativity: A Thermal Equivalence Principle
by Riccardo Fantoni
Quantum Rep. 2026, 8(2), 42; https://doi.org/10.3390/quantum8020042 - 1 May 2026
Viewed by 210
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Topic Path Integral Monte Carlo on Riemannian Manifolds)
11 pages, 571 KB  
Article
Verifying Quantum Network Nonlocality Based on the Extended Mermin Inequality
by Xinyue Li, Yan-Han Yang and Ming-Xing Luo
Quantum Rep. 2026, 8(2), 41; https://doi.org/10.3390/quantum8020041 - 1 May 2026
Viewed by 193
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Topic Quantum Computing: Latest Advances and Prospects)
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18 pages, 5289 KB  
Article
Ultrafast Helicity-Controlled Spin Dynamics in Curved Time: A Photonic Pathway to Geometry-Driven Spin Transport
by Mohammad Mohammadiaria
Quantum Rep. 2026, 8(2), 40; https://doi.org/10.3390/quantum8020040 - 1 May 2026
Viewed by 261
Abstract
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 [...] Read more.
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. Full article
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9 pages, 777 KB  
Article
Experimental Proof That Bell’s Inequality Cannot Falsify Local Realism, Together with Corresponding Cause Analysis and Conjectures
by Ting Zhou
Quantum Rep. 2026, 8(2), 39; https://doi.org/10.3390/quantum8020039 - 25 Apr 2026
Viewed by 926
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Quantum Precision Measurement)
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25 pages, 332 KB  
Article
From Proportional Stationarity to Curvature–Strain Balance: A Variational Bridge for Equilibrium Ratios
by Robert Castro
Quantum Rep. 2026, 8(2), 38; https://doi.org/10.3390/quantum8020038 - 22 Apr 2026
Viewed by 241
Abstract
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 [...] Read more.
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. Full article
48 pages, 1752 KB  
Article
Quantum Image Representation with Enhanced Intensity Preservation and Fidelity (IP-QIR)
by Vrushali Nikam, Shirish Sane and Manish Motghare
Quantum Rep. 2026, 8(2), 37; https://doi.org/10.3390/quantum8020037 - 22 Apr 2026
Viewed by 260
Abstract
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 [...] Read more.
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. Full article
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36 pages, 3212 KB  
Review
Bipolar Entropy vs. Entropy/Negentropy: From Quantum Emergence to Agentic AI&QI with Collectively Entangled Bipolar Strings ER ≥≥ EPR
by Wen-Ran Zhang and Hengyu Zhang
Quantum Rep. 2026, 8(2), 36; https://doi.org/10.3390/quantum8020036 - 20 Apr 2026
Viewed by 1361
Abstract
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) [...] Read more.
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. Full article
(This article belongs to the Topic Topological, Quantum, and Molecular Information Approaches to Computation and Intelligence)
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21 pages, 1173 KB  
Article
Quantum Correlations in Classical Systems
by Ghenadie N. Mardari
Quantum Rep. 2026, 8(2), 35; https://doi.org/10.3390/quantum8020035 - 18 Apr 2026
Viewed by 1527
Abstract
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 [...] Read more.
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. Full article
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29 pages, 450 KB  
Article
Quantum-Informational History Optimization Theory (QIHOT): A Single-History Selection Framework with Consistency Results
by Freeman Hui
Quantum Rep. 2026, 8(2), 34; https://doi.org/10.3390/quantum8020034 - 16 Apr 2026
Viewed by 470
Abstract
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 [...] Read more.
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. Full article
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66 pages, 5999 KB  
Article
Copy-Time Geometry from Gauge-Coded Quantum Cellular Automata: Emergent Gravity and a Golden Relation for Singlet-Scalar Dark Matter
by Mohamed Sacha
Quantum Rep. 2026, 8(2), 33; https://doi.org/10.3390/quantum8020033 - 13 Apr 2026
Viewed by 1668
Abstract
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 [...] Read more.
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. Full article
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24 pages, 2681 KB  
Article
The Informational Economy Functional: A Variational Principle for Decoherence and Classical Emergence
by Wan Zheng
Quantum Rep. 2026, 8(2), 32; https://doi.org/10.3390/quantum8020032 - 10 Apr 2026
Viewed by 487
Abstract
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 [...] Read more.
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. Full article
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16 pages, 309 KB  
Article
Fixed Spectral Data and the Dynamics of Spacetime Geometry
by Jacob Yan Gurevich
Quantum Rep. 2026, 8(2), 31; https://doi.org/10.3390/quantum8020031 - 8 Apr 2026
Viewed by 663
Abstract
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 [...] Read more.
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. Full article
24 pages, 9432 KB  
Article
QGeo: A Python Package for Calculating Geodesic Control Functions for Quantum Computing
by Sean T. Crowe, Joshua J. Leiter, John P. T. Stenger, Zachary L. Barvian, Joseph A. Diaz, Shoshana Kinzel, Joanna N. Ptasinski and Daniel Gunlycke
Quantum Rep. 2026, 8(2), 30; https://doi.org/10.3390/quantum8020030 - 1 Apr 2026
Viewed by 547
Abstract
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. [...] Read more.
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. Full article
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12 pages, 274 KB  
Article
A Derivation of the Entangled State Representation by the Slice Theorem of the Wigner Operator
by Ke Zhang and Hongyi Fan
Quantum Rep. 2026, 8(2), 29; https://doi.org/10.3390/quantum8020029 - 26 Mar 2026
Viewed by 336
Abstract
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 [...] Read more.
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. Full article
17 pages, 342 KB  
Article
Optimality of Quantum Adiabatic Search Algorithm and Its Circuit Model
by Jie Sun, Zhimin Zhang and Songfeng Lu
Quantum Rep. 2026, 8(2), 28; https://doi.org/10.3390/quantum8020028 - 26 Mar 2026
Viewed by 570
Abstract
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 [...] Read more.
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. Full article
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