Phase Accumulation and Environmental Distinguishability in Quantum-to-Classical Transition Systems

David Wert

Published May 13, 2026• 0 citations

Abstract

The quantum-to-classical transition is commonly described through decoherenceand environmental entanglement, yet quantitative measures of structured phaseorganisation within coherent quantum states remain comparatively underdeveloped.This work introduces a phase-organisation functional that measures the structuredphase separation encoded in the off-diagonal coherence channels of a quantumdensity matrix. The functional characterises the progressive conversion ofcoherent phase structure into environmentally encoded branch distinguishabilityduring open-system evolution. A minimal two-state model illustrates the evolution of phase organisation underdecoherence. Environmental degrees of freedom are modelled as distributedphase-encoding channels whose cumulative phase dispersion suppresses coherenceexponentially. An effective informational persistence quantity, termedinformational mass (Imass), is introduced operationally as a measure ofaccumulated environmental branch distinguishability. The framework connects phase accumulation, decoherence, entropy growth, andclassical distinguishability within a unified informational description whileremaining fully compatible with standard open quantum systems theory. Potentialapplications to coherence monitoring and hybrid quantum-classical architecturesare discussed. This is a working paper deposited to establish a citable DOI record.The framework is exploratory; limitations and open questions arediscussed explicitly in the paper. Part of the Q2C Research Initiative theoretical series. This paper establishes the phase-organisation functional and single-threshold Imass criterion as the foundational framework for the programme. Paper 2 (dual-parameter threshold structure, spectral Imass, entropy plateau conditions, and Mpemba-like trajectory crossings) is available at https://doi.org/10.5281/zenodo.20531722. Paper 3 (σ-algebra filtration structure) is in preparation.

DOI: 10.5281/zenodo.20167963

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Abstract

DOI: 10.5281/zenodo.20167963

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\ (\left\langle p(t) \right\rangle,\left\langle x(t) \right\rangle)

and for the ground covariance matrix establish a direct connection between microscopic environmental properties, classical-like trajectories and the QPS geometry. The proposed framework provides a unified theoretical foundation for modeling decoherence in nanoscale systems involving simultaneous position and momentum interactions with the environment. The QPS framework may thus bridge fundamental theory and practical quantum engineering, offering a promising coherent pathway to understand, control, and exploit decoherence at the nanoscience frontier.