This archive contains the third paper in a coherent three-paper research trilogy examining how quantum structure is reflected in classical measurement statistics under noise. The paper introduces the Principle of Selective Transcription, which explains when and why quantum structural properties can survive noise as distinguishable classical statistics. It formalizes classical observability as a pipeline-dependent notion determined by the combined action of the noise channel, measurement basis, and classical feature extraction. On this basis, the paper introduces a taxonomy of quantum structure as robustly transcribable, fragilely transcribable, or intrinsically invisible. The work synthesizes and explains the empirical findings of the first two papers in the trilogy, accounting for conditional survival, ordered feature collapse, basis dependence, and regimes of diagnostic blindness. The framework is validated by a minimal analytical example (a two-qubit Bell state) and a targeted numerical confirmation demonstrating basis-dependent reversal of feature collapse ordering. This paper provides the conceptual capstone of the trilogy, offering an explanatory framework for classical observability in noisy quantum systems and clarifying fundamental limits on classical information extraction from quantum states.
This archive contains the third paper in a coherent three-paper research trilogy examining how quantum structure is reflected in classical measurement statistics under noise. The paper introduces the Principle of Selective Transcription, which explains when and why quantum structural properties can survive noise as distinguishable classical statistics. It formalizes classical observability as a pipeline-dependent notion determined by the combined action of the noise channel, measurement basis, and classical feature extraction. On this basis, the paper introduces a taxonomy of quantum structure as robustly transcribable, fragilely transcribable, or intrinsically invisible. The work synthesizes and explains the empirical findings of the first two papers in the trilogy, accounting for conditional survival, ordered feature collapse, basis dependence, and regimes of diagnostic blindness. The framework is validated by a minimal analytical example (a two-qubit Bell state) and a targeted numerical confirmation demonstrating basis-dependent reversal of feature collapse ordering. This paper provides the conceptual capstone of the trilogy, offering an explanatory framework for classical observability in noisy quantum systems and clarifying fundamental limits on classical information extraction from quantum states.
This repository contains the source files for the paper: Irreversibility and Ordering in Classical Observability of Quantum Structure The paper develops a formal framework explaining when and why classical statistics extracted from noisy quantum systems retain architecture-dependent information, and when they inevitably lose it. Building on a trilogy of earlier empirical and operational studies, the work introduces the diagnostic pipeline as a fundamental object of analysis: a fixed composition of a noise channel, a measurement choice, and a deterministic classical feature map. Such pipelines are shown to form a preorder under information-degrading transformations, induced by standard monotonicity principles. Within this framework, several phenomena observed empirically are shown to be structural necessities rather than numerical accidents: Feature-dependent collapse arises from deterministic feature post-processing below the identity (full-distribution) pipeline. Basis-dependent diagnostic blindness corresponds to incomparability between pipelines using different fixed measurement bases. Irreversible loss of distinguishability follows from genuine noise degradation and cannot be undone by downstream measurement or feature choices. The paper proves general monotonicity results, establishes generic incomparability of measurement bases, and derives falsifiable predictions linking noise–basis alignment to collapse thresholds for population-encoded distinctions. Minimal empirical consistency checks against the companion trilogy datasets are provided. The framework yields practical design principles for lightweight diagnostics in NISQ-era experiments, clarifying fundamental limits on classical access to quantum structure under realistic constraints. Contents Irreversibility_and_Ordering_in_Classical_Observability_of_Quantum_Structure.pdfFinal compiled manuscript. Irreversibility_and_Ordering_in_Classical_Observability_of_Quantum_Structure.texLaTeX source (self-contained; bibliography and figures embedded). Relation to Other Work This paper provides the formal, structural foundation for a companion trilogy on architecture-sensitive classical fingerprints under noise, including: Feature-dependent collapse under fixed pipelines Basis-dependent diagnostic blindness Selective transcription as an operational principle The present work unifies and explains these results within a single information-theoretic preorder framework. Status Submission-ready manuscript.Intended for submission to a peer-reviewed journal in quantum information theory. Licence See LICENSE.
This repository accompanies the preprint “Mapping the Limits of Architecture-Sensitive Noise Fingerprints in Quantum States.” The work investigates when and why simple classical measurement statistics obtained from noisy quantum systems retain information about the underlying quantum state architecture, and when such information collapses entirely. Building on earlier results demonstrating the existence of architecture-dependent classical fingerprints for stabilizer states under local noise, this study systematically maps the boundaries and failure modes of that phenomenon. Using exact probability distributions for small-to-moderate system sizes, we introduce controlled departures from stabilizer structure and track the degradation of classical features under dephasing and depolarizing noise. The analysis reveals sharply conditional survival of architecture sensitivity, a consistent feature-dependent collapse ordering, and a strong dependence on measurement basis and perturbation geometry. In particular, regimes of genuine diagnostic blindness are identified, where classical statistics become architecture-indistinguishable even though the underlying quantum states remain highly structured. The archive includes the full manuscript (PDF and LaTeX source), all figures appearing in the paper, the scripts required to reproduce the numerical experiments and figures, and the corresponding data outputs. All results are based on exact numerical evaluation (no sampling, optimisation, tomography, or machine learning). The work is intended as a lightweight, diagnostic limits study, providing practical guidance on when simple classical measurements are informative and when their use is fundamentally unreliable. Together with the companion papers in this series, the repository contributes to a coherent empirical and theoretical programme on the classical observability of quantum structure under noise.Version 1.1 notes.This revision clarifies the collapse criterion used to define architecture indistinguishability, explicitly specifies numerical precision and robustness checks, and adds a qualitative reliability chart summarising when different classical features remain informative. The presentation of noise-model dependence, system-size stability, and perturbation geometry has been sharpened, and the relationship to companion papers in the series has been made explicit. No new phenomena are introduced; the update improves transparency, interpretability, and practical usability of the results.
This mini-monograph proposes a new variational and information-geometric framework for understanding the quantum measurement problem, with particular emphasis on the unresolved problem of outcome selection. While decoherence theory explains the suppression of interference and the emergence of stable pointer bases, it does not by itself explain why one definite outcome is realized rather than another. This work argues that the missing element is not simply an additional dynamical mechanism, but a structural principle of selection. The central thesis is that quantum measurement may be understood as a process of entropic channel selection within a structured space of admissible outcomes. Drawing on Schrödinger bridge theory, entropy-regularized optimal transport, stochastic path-space variational principles, concentration of measure, and large deviation theory, the monograph develops a framework in which collapse-like definiteness emerges through constrained probabilistic evolution. Measurement is thereby reinterpreted not as an arbitrary interruption of unitary dynamics, but as a threshold phenomenon in the geometry of information. The work introduces an informational configuration space of possible resolution channels, defines an entropic action functional over stochastic paths, and proposes a channel-selection principle based on entropy-minimizing interpolation. It further examines the relation between Schrödinger bridges and optimal transport, explores the zero-noise limit, connects the framework to path-integral intuition, and develops explicit models of Gaussian bridge dynamics and two-channel selection. The emergence of classicality is treated through exponential concentration, threshold amplification, and phase-transition-like stabilization in high-dimensional systems. The monograph does not claim to replace standard quantum mechanics. Rather, it seeks to clarify how definite outcomes might arise from variational organization within probability itself, while remaining compatible with reduced quantum dynamics, decoherence, and open-system evolution. It is intended as a conceptual and mathematical foundation for further work at the intersection of quantum foundations, stochastic processes, information geometry, and the theory of emergent classicality.
This archive accompanies the paper Architecture-Sensitive Noise Fingerprints in Classical Statistics of Quantum States. It contains the full manuscript, all figures appearing in the paper, and the Python scripts used to generate the numerical results. The project demonstrates that classical measurement statistics obtained from noisy quantum states retain reproducible, architecture-dependent structure. Even under standard local, Markovian noise models, simple low-order classical features—such as entropy, maximum probability, parity mass, and Hamming-weight distributions—encode diagnostic fingerprints of the underlying quantum state architecture. The analysis focuses on stabilizer states (including GHZ, cluster, and star graph states), fixed measurement bases, and exact probability distributions. No machine learning, optimisation, tomography, or state reconstruction is used. All results are generated using transparent, reproducible numerical simulations. The contents of this archive are: LaTeX source and compiled PDF of the manuscript All figures used in the paper (PDF/PNG) Python scripts for generating the figures and classical feature data A README describing structure and reproducibility This archive is intended to support transparency, reproducibility, and reuse of the results, and may serve as a lightweight reference for diagnostic approaches to quantum noise and state architecture.
These exploratory papers investigated distributional effects of decoherence in GHZ states. While several interesting observations were made, unresolved inconsistencies and lack of analytical grounding led us to treat these as internal exploratory work. Key conceptual lessons from these studies informed later, more general work on selective transcription.This archive contains a short research paper titled “Distributional Effects of Local Decoherence on GHZ Measurement Statistics.” The paper studies how local dephasing noise affects the full measurement outcome distributions of Greenberger–Horne–Zeilinger (GHZ) states when coherence is probed using a fixed rotated measurement basis. Rather than focusing on reduced density matrices or expectation values, the work analyzes decoherence at the level of empirical outcome histograms, using Jensen–Shannon divergence (JSD) as a bounded, information-theoretic metric. The central result is that, when GHZ states subjected to local dephasing are measured in a coherence-sensitive basis (implemented via a global Hadamard transformation prior to readout), the resulting outcome distribution exhibits a non-monotonic divergence from an ideal reference distribution. This divergence vanishes in both the fully coherent and fully dephased limits and attains a pronounced maximum at intermediate decoherence strength. The height and sharpness of this maximum increase with the number of qubits, reflecting the collective fragility of global coherence in GHZ states. The paper emphasizes that this effect does not arise for computational-basis measurements aligned with the dephasing channel, nor for product states or classical mixtures with matched marginals. The observed non-monotonicity therefore constitutes an operational signature of global multipartite coherence, rather than a generic consequence of noise or finite sampling. The archive includes: The complete LaTeX source of the paper. The compiled PDF. Figure files illustrating the Jensen–Shannon divergence curves. A short script used to generate the figures. The work is intended as a minimal, reproducible, and experimentally relevant diagnostic for coherence loss on noisy intermediate-scale quantum (NISQ) devices. It makes no interpretational claims and does not rely on state tomography, requiring only standard GHZ preparation, local dephasing, a fixed basis rotation, and histogrammed measurement outcomes.
Recommended reading order Paper I — Core FrameworkStructural Constraints on Realizable Physical Transitions Paper II — Empirical Validation (Ordering)Structural Ordering of Observable Noise in Fixed-Workload Quantum Circuits Paper III — Empirical Validation (Topology & Holonomy)Topology-Dependent Realizability Under Fixed Quantum Dynamics The papers are intended to be read in this sequence. This record contains the complete Aionics trilogy, a coordinated set of three research papers establishing and empirically validating a constraint-based framework for physical realizability. The first paper introduces Aionics, a pre-dynamical framework in which structural constraints delimit which physical transitions are realizable, with time emerging as an ordering of realized transitions rather than as a fundamental substrate. The second paper provides empirical evidence for this framework by demonstrating monotonic ordering of observable noise by structural organization under fixed quantum dynamics, defeating gate-count and workload-based null models. The third paper extends these results by establishing topology-dependent realizability: circuits matched in workload and scalar structure but differing in interaction topology exhibit stable, reproducible differences in observable entropy, demonstrating holonomy and path dependence. Together, these works show that structure is an operationally measurable constraint on physical realizability, supplementing standard dynamical descriptions without modifying existing physical laws.