A Proof of Shor's Orthogonal-Measurement Conjecture and the Structure of Information-Optimal Quantum Measurements

Abstract:Which quantum measurement extracts the most classical information from an ensemble? We introduce the posterior algebra, a new canonical operator algebra selected by mutual information. For faithful ensembles, an affine information bound is exact precisely when this algebra is commutative; its joint spectral measurement is then optimal, and every optimal finite POVM refines it. Binary ensembles have one generator; compactness covers singular states, giving a proof of Shor's finite-dimensional binary orthogonal-measurement conjecture. The framework also gives rigidity bounds and a certified posterior-spectral receiver, validated on 408 mixed-state instances.

11 pages, 1 figure. This work was already publicly available on Zenodo by 13 August 2026, prior to this arXiv submission: this https URL

arXiv:2609.27992 [quant-ph]

(or arXiv:2609.27992v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.27992 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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