Quantum Reports

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. Full article

The photonic spin Hall effect (PSHE) originates from the spin–orbit interaction (SOI) of light. The literature indicates that the transverse spin-dependent shift, ${\delta }_H^{-}$ (SDS), from the PSHE is weak (in the nanometer range) and difficult to measure directly. This study utilizes a plasmonic structure to improve the ${\delta }_H^{-}$ in the PSHE. The obtained results of this study demonstrate that the inclusion of silicon nitride (Si₃N₄) significantly enhances the ${\delta }_H^{-}$ relative to its absence; however, plasmonic material is present in both cases. The enhanced shifts exhibit a significant dependence on the resonance angle (${\theta }_r$) and the thickness of layers of the PSHE structure to attain the maximum increase in ${\delta }_H^{-}$ 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 ${\delta }_H^{-}$ 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 ${\delta }_H^{-}$ 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. Full article

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). Full article

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 $\varsigma \left(x\right)$, 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 $A(\psi ,\nabla \psi )=1-{\varsigma }^2(\psi ,\nabla \psi )$ 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 $R_{\mu \nu }^{\mathrm{eff}}=R_{\mu \nu }+f_{\mu \nu }$, where the correction $f_{\mu \nu }$ is expressed in terms of derivatives of $\mathsf{\Phi }=ln(1-{\varsigma }^2)$ 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. Full article

The position operator $\widehat{r}$ appears as $i{\partial }_p$ 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 $\widehat{r}$ by $i{\partial }_p$ to $i{\sum }_j{\partial }_{k_j}$, 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., $r_{m,n}=r_{n,m}^{*}\nLeftrightarrow \widehat{r}={\widehat{r}}^{†}$, 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. Full article

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. Full article

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. Full article

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. Full article

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-T_c 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-T_c 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. Full article

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. Full article

Bell–CHSH is an inequality about unconditional expectations: under measurement independence, Bell locality, and bounded outcomes, the CHSH value satisfies $S\le 2$. 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 $\gamma (a,b,\lambda )\in [0,1]$ and the resulting accepted hidden-variable law ${\nu }_{ab}$ obtained by weighting the measurement-independent prior $\rho$ by $\gamma$ and renormalizing. If ${\nu }_{ab}$ 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 $S_{\mathrm{obs}}>2$ by selection alone. We quantify the required setting dependence in total variation (TV) distance. For any reference law $\mu$ we prove the sharp bound $S_{\mathrm{obs}}\le 2+2{\sum }_{q\in Q}\mathrm{TV}({\nu }_q,\mu )$ for a CHSH quartet Q. Optimizing over $\mu$ yields the intrinsic dispersion bound $S_{\mathrm{obs}}\le 2+2{\Delta }_Q$, and, in particular, $S_{\mathrm{obs}}\le min\{4,2+6D_Q\}$, where $D_Q$ is the quartet TV diameter. The constants are optimal. Consequently, reproducing Tsirelson’s value $2\sqrt{2}$ within Bell-local measurement-independent models via setting-dependent acceptance requires ${\Delta }_Q\ge \sqrt{2}-1$ (hence, $D_Q\ge (\sqrt{2}-1)/3$). 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 ${\Delta }_{Q,X}$ computable by linear programming on finite tag alphabets. Full article

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. Full article

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. Full article

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: S_core (a collapsed entropy core from configurational mass), S_EM (a structured electromagnetic entropy field from charge), and S_thermal (a diffuse entropy component from ambient interactions). We show that spin emerges as a rotating S_EM shell around S_core, 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. Full article

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. Full article

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 $A\ast B=AB+\epsilon \omega (A,B)$, where $\omega$ is a Hochschild 2-cocycle. We interpret $\omega$ 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 $\mathcal{O}\left({\epsilon }^2\right)$ 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 $\epsilon$ 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. Full article

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 ${\mathrm{\Phi }}_{\mu }$ 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. Full article

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. Full article

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. Full article