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Beyond Shor's Conjecture: Optimal Quantum Measurements at Fixed Error

Year: 2026

Type: preprint

Abstract: We prove Shor's conjecture: an orthogonal measurement maximizes the information obtainable from any two quantum states in finite dimension. We then show that an error constraint can require three outcomes. For a class of full-rank qubit pairs, the best orthogonal basis switches abruptly as the error penalty increases. Near the switch, three outcomes yield more information at the same error than any orthogonal measurement or random mixture of them. The extra outcome distinguishes confidence levels in one guess; every outcome is used.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.27992

Authors: Wang, Jinbo, Wang, Qihang, Hou, Pengcheng, Chen, Kun

Institutions: Peking University, Chinese Academy of Sciences, Institute of Theoretical Physics

Language: English

Topic: Quantum Information and Cryptography

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214159094

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