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Universal Decision Principle from Local Relative Entropy Flux: A Detector Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED

Venkatesan Narayanaswamy

Published Jan 2, 2026• 0 citations
Publisher

Abstract

Preprint and reproducibility bundle for: “Universal Decision Principle from Local Relative Entropy Flux: A Detector-Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED”. Contents: (1) Manuscript PDF (preprint). (2) Reproducibility bundle (ZIP): literature-derived spreadsheets and figure artefacts, analysis scripts/parameter manifests, and Lean 4/mathlib verification artefacts. Submitted to Physical Review A (TempID: es2026jan01_605). arXiv identifier will be added after arXiv posting.

DOI
10.5281/zenodo.18124826

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Universal Decision Principle from Local Relative Entropy Flux: A Detector Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED

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We propose an operational, detector-consistent criterion for identifying when and where a quantum interaction produces a stable classical record. The criterion—termed the Universal Decision Principle (UDP)—is defined from instrument-fixed maps rather than ad hoc collapse parameters and is formulated to remain meaningful from finite-dimensional quantum mechanics to local algebraic quantum field theory (AQFT) and gauge-invariant inclusive quantum electrodynamics (QED). Given an underlying state , an admissible operational reduction to a detector region/channel , and an instrument-defined pointer channel onto a commuting record algebra, we define the pointer-relative entropy where is the Umegaki relative entropy in finite settings and the Araki–Uhlmann relative entropy on local von Neumann algebras in AQFT. In record-formation regimes decreases towards zero; we therefore localise the event by the relative-entropy flux and declare record formation at the statistically significant interior maximum of within an a priori specified analysis window. The protocol is explicitly falsifiable through nonparametric bootstrap confidence intervals, structure-preserving surrogate tests, sensitivity stability gates, and detector timing/jitter budgets; irreversibility is graded independently using data-processing inequality remainders and Petz/universal recovery performance near . We provide domain-specific constructions of and for (i) interferometric and spin measurements, (ii) Mott-type track formation as sequential cellwise events, (iii) local AQFT causal regions, and (iv) gauge-consistent inclusive QED channels. Supplementary materials include literature-derived datasets, analysis spreadsheets and figures, and machine-checkable formal verification artefacts (mathlib) supporting key logical steps.

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This record archives version v1.3 of the manuscript “Unified Residual Classicality Criterion for the Quantum-to-Classical Transition” and its full reproducibility package. This version is the repository companion to the journal-submission version prepared for Quantum Studies: Mathematics and Foundations. It includes the main manuscript, supplementary mathematical notes, supplementary validation report, figure source archive, LaTeX/source archive, benchmark CSV files, Python scripts, manifest files, citation metadata, license file, checksums, and author declarations. The work proposes a falsifiable, comparator-dependent residual-vector criterion for assessing quantum-to-classical behaviour. Classicality is certified only when predeclared residual channels — dynamical, semiclassical, operational, coarse-graining, and open-system — simultaneously pass their declared tolerances for a specified comparator, observable class, resolution, norm, and finite time interval. The work does not claim a universal solution to the measurement problem or a universal proof of quantum-to-classical emergence; it provides a finite-time certification framework with sufficient error-control conditions and controlled benchmark validation. Version-specific DOI: 10.5281/zenodo.20750070Previous version DOI: 10.5281/zenodo.20682081

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ECEG V9: the submitted manuscript, editable LaTeX source and computational supplement. This repository deposit was created on 31 October 2026 to preserve a dated, DOI-identified copy. The manuscript and accompanying scientific files are unchanged from the Quantum Information Processing submission of 10 October 2026. This is a preprint, not an accepted or peer-reviewed publication. Full text and supplementary files are restricted; bibliographic metadata are public. AbstractQuantum records can encode different source observables while sharing the same reduced states and energy statistics. We determine the optimal fidelity for converting a family of such records using local diagonal controls on an arbitrary interaction hypergraph. The answer depends only on the branch overlap and the smallest unsupported interaction. A weighted phase inequality proves the optimum and supplies an attaining control. We also derive limits on shared access to records, distinguish equal endpoint marginals from stationary evolution, and extend the fidelity bound to mixed preparation errors and integrated control deviations. All results concern a specified finite-dimensional quantum model. FilesECEG_V9_QIP_Submitted.pdf: submitted English manuscript (18 pages).ECEG_V9_QIP_Source.zip: editable LaTeX source and template files.ESM_1.zip: numerical verification scripts, machine-readable results, reproducibility instructions and file manifest. The statement in the submitted manuscript that no public repository identifier was claimed describes the submission on 10 October 2026; the present DOI identifies this later archival deposit.

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Preprint and reproducibility bundle for: “Universal Decision Principle from Local Relative Entropy Flux: A Detector-Consistent, Falsifiable Criterion for Quantum Record Formation across QM, Mott Tracks, AQFT, and QED”. Contents: (1) Manuscript PDF (preprint). (2) Reproducibility bundle (ZIP): literature-derived spreadsheets and figure artefacts, analysis scripts/parameter manifests, and Lean 4/mathlib verification artefacts. Submitted to Physical Review A (TempID: es2026jan01_605). arXiv identifier will be added after arXiv posting.
We propose an operational, detector-consistent criterion for identifying when and where a quantum interaction produces a stable classical record. The criterion—termed the Universal Decision Principle (UDP)—is defined from instrument-fixed maps rather than ad hoc collapse parameters and is formulated to remain meaningful from finite-dimensional quantum mechanics to local algebraic quantum field theory (AQFT) and gauge-invariant inclusive quantum electrodynamics (QED). Given an underlying state , an admissible operational reduction to a detector region/channel , and an instrument-defined pointer channel onto a commuting record algebra, we define the pointer-relative entropy where is the Umegaki relative entropy in finite settings and the Araki–Uhlmann relative entropy on local von Neumann algebras in AQFT. In record-formation regimes decreases towards zero; we therefore localise the event by the relative-entropy flux and declare record formation at the statistically significant interior maximum of within an a priori specified analysis window. The protocol is explicitly falsifiable through nonparametric bootstrap confidence intervals, structure-preserving surrogate tests, sensitivity stability gates, and detector timing/jitter budgets; irreversibility is graded independently using data-processing inequality remainders and Petz/universal recovery performance near . We provide domain-specific constructions of and for (i) interferometric and spin measurements, (ii) Mott-type track formation as sequential cellwise events, (iii) local AQFT causal regions, and (iv) gauge-consistent inclusive QED channels. Supplementary materials include literature-derived datasets, analysis spreadsheets and figures, and machine-checkable formal verification artefacts (mathlib) supporting key logical steps.
This record archives version v1.3 of the manuscript “Unified Residual Classicality Criterion for the Quantum-to-Classical Transition” and its full reproducibility package. This version is the repository companion to the journal-submission version prepared for Quantum Studies: Mathematics and Foundations. It includes the main manuscript, supplementary mathematical notes, supplementary validation report, figure source archive, LaTeX/source archive, benchmark CSV files, Python scripts, manifest files, citation metadata, license file, checksums, and author declarations. The work proposes a falsifiable, comparator-dependent residual-vector criterion for assessing quantum-to-classical behaviour. Classicality is certified only when predeclared residual channels — dynamical, semiclassical, operational, coarse-graining, and open-system — simultaneously pass their declared tolerances for a specified comparator, observable class, resolution, norm, and finite time interval. The work does not claim a universal solution to the measurement problem or a universal proof of quantum-to-classical emergence; it provides a finite-time certification framework with sufficient error-control conditions and controlled benchmark validation. Version-specific DOI: 10.5281/zenodo.20750070Previous version DOI: 10.5281/zenodo.20682081
ECEG V9: the submitted manuscript, editable LaTeX source and computational supplement. This repository deposit was created on 31 October 2026 to preserve a dated, DOI-identified copy. The manuscript and accompanying scientific files are unchanged from the Quantum Information Processing submission of 10 October 2026. This is a preprint, not an accepted or peer-reviewed publication. Full text and supplementary files are restricted; bibliographic metadata are public. AbstractQuantum records can encode different source observables while sharing the same reduced states and energy statistics. We determine the optimal fidelity for converting a family of such records using local diagonal controls on an arbitrary interaction hypergraph. The answer depends only on the branch overlap and the smallest unsupported interaction. A weighted phase inequality proves the optimum and supplies an attaining control. We also derive limits on shared access to records, distinguish equal endpoint marginals from stationary evolution, and extend the fidelity bound to mixed preparation errors and integrated control deviations. All results concern a specified finite-dimensional quantum model. FilesECEG_V9_QIP_Submitted.pdf: submitted English manuscript (18 pages).ECEG_V9_QIP_Source.zip: editable LaTeX source and template files.ESM_1.zip: numerical verification scripts, machine-readable results, reproducibility instructions and file manifest. The statement in the submitted manuscript that no public repository identifier was claimed describes the submission on 10 October 2026; the present DOI identifies this later archival deposit.
Why does quantum relative entropy occupy such a privileged role among measures of distinguishability? We show that a single operational principle determines it. If one pair of states can be distinguished at least as successfully as another for every prior, when both are assisted by the same auxiliary pair, acting as a catalyst, a distinguishability measure should assign it no smaller value. Remarkably, for a normalized measure, this requirement singles out Umegaki relative entropy under mild classical continuity and expansibility on uniform distributions: adding impossible outcomes leaves their associated entropy unchanged. Qubit catalysts already suffice. No additivity or quantum continuity is assumed. We also prove that, without auxiliary assistance, respecting binary discrimination dominance uniquely determines the quantum extension of every regular classical divergence, including the Hirche--Tomamichel extensions of classical fff-divergences. For additive classical divergences, these extensions respect classical catalysis; allowing noncommuting qubit catalysts is what singles out Umegaki relative entropy.
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves especially useful near equilibrium. However, this bound tends to be irrelevant in general nonequilibrium situations. We propose a new upper bound for such fluxes in terms of quantum relative entropy, applicable even far from equilibrium and in the strong coupling regime. Additionally, we compare this bound with Monte Carlo simulations of random qubits with coherence, as well as with a model of two interacting nuclear spins.