Irreversibility and Ordering in Classical Observability of Quantum Structure

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.