Quantum Reports

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

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

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

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

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

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

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

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

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

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

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

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

We develop the binary-shadow method for exact CNOT counting and apply it to arbitrary wire permutations. The Heisenberg evolution of rotated local Z observables converts every CNOT gate into an elementary transvection over ${\mathbb{F}}_2$, and for a wire permutation, the resulting binary shadow is rigid: it must equal the associated permutation matrix. This reduces the exact CNOT cost of a wire permutation in the CNOT+local model to the transvection length of its permutation matrix. The remaining problem is classical. The relevant mathematical input is the transvection-length theory of permutation matrices, or equivalently, the CNOT-only synthesis of permutation circuits. Combining the binary-shadow reduction with the graph-theoretic link-middle-cut theorem for cycle matrices yields an exact formula: if $\sigma \in S_n$ has $c\left(\sigma \right)$ disjoint cycles, then $\mathrm{CNOT-cost}\left(W_{\sigma }\right)={\mathsf{\ell }}_{\mathrm{tr}}\left(P_{\sigma }\right)=3\left(n-c\left(\sigma \right)\right).$ The novelty is therefore not the CNOT-only permutation formula by itself, but the transfer of that exact lower bound to the CNOT+local model: arbitrary one-qubit gates may rotate the local Pauli axes, but they cannot reduce the CNOT count of a wire permutation. In particular, the n-qubit cyclic SWAP gate $S_n|x_1{⟩}_1|x_2{⟩}_2\cdots |x_n{⟩}_n=|x_n{⟩}_1|x_1{⟩}_2\cdots {|x_{n-1}⟩}_n$ requires exactly $3(n-1)$ CNOT gates, even when arbitrary one-qubit gates are allowed at zero cost. Thus, the exact values for $n=2,3,4,5,6,\dots$ are $3,6,9,12,15,\dots$. We also give explicit optimal factorizations for $n=4$ and $n=5$, and show more generally that each additional wire in a cyclic shift costs exactly three more CNOT gates. Full article

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

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

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

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

Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including $1/f$ charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing ($T_2^{*}$) dynamics, they fail to account for energy relaxation ($T_1$) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing. Full article