Quantum Rep., Volume 8, Issue 1 (March 2026) – 27 articles

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

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

This work presents the Theory of Spacetime Impedance (TSI), a phenomenological framework in which the vacuum is modeled as a distributed reactive medium with an effective RLC structure. At the classical level, the vacuum is characterized by permeability, ${\mu }_0$, permittivity, ${\epsilon }_0$, and impedance, $Z_0$, so that the speed of light follows from the vacuum’s constitutive reactive properties. The TSI introduces a reactive–dissipative term, $R_H$, as an effective mechanism associated with irreversibility, decoherence, and entropy production, providing a physical basis for the arrow of time. At the quantum level, TSI incorporates a quantum RLC triad associated with the electron, defined by quantum inductance, $L_K$, quantum capacitance, $C_K$, and von Klitzing resistance, $R_K$. When normalized by the Compton wavelength, these quantities admit a direct comparison with ${\mu }_0$ and ${\epsilon }_0$, identifying the fine-structure constant as an impedance scaling factor between classical and quantum regimes. Within this unified reactive picture, inductive, capacitive, and resistive responses are respectively associated with gravitation, electromagnetism, and thermodynamic irreversibility, offering a complementary bridge across quantum, relativistic, and macroscopic domains. Full article

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

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

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

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

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

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

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