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arXiv · 2609.27992

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

Jinbo Wang·Qihang Wang·Kun Chen
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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.

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Jinbo Wang, Qihang Wang, Kun Chen. 2026-09-23. A Proof of Shor's Orthogonal-Measurement Conjecture and the Structure of Information-Optimal Quantum Measurements. https://arxiv.org/abs/2609.27992

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