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

arXiv:2609.27992 · quant-ph, math-ph, math.MP · Submitted 2026-09-23 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Regret — 6× in this paper · explained in 3 episodes
• Benchmark — 5× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Analyzer — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Information Gain — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• On the Number of Elements Needed in a POVM Attaining the Accessible Information
• Proof of the Orthogonal Measurement Conjecture for Qubit States
• On Shor's conjecture on the accessible information of quantum dichotomies
• Uhlmann's theorem for measured divergences
• On maximization of measured $f$-divergence between a given pair of quantum states

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