发表机构
School of Mathematical Sciences, Peking University; Institute of Theoretical Physics, Chinese Academy of Sciences（北京大学数学科学学院; 中国科学院理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出后验代数框架，证明Shor有限维二元正交测量猜想，并给出信息最优量子测量的结构、刚性界及经认证的后验谱接收机，在408个混合态实例上验证。
AI 中文摘要
哪种量子测量能从系综中提取最多的经典信息？我们引入了后验代数，这是一种由互信息选择的新典范算子代数。对于忠实系综，仿射信息界恰好精确当且仅当该代数是交换的；其联合谱测量此时是最优的，且每个最优有限POVM都细化它。二元系综有一个生成元；紧致性覆盖奇异态，从而给出了Shor有限维二元正交测量猜想的一个证明。该框架还给出了刚性界和一个经认证的后验谱接收机，并在408个混合态实例上进行了验证。
英文摘要
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.
Comments11 pages, 1 figure. This work was already publicly available on Zenodo by 13 August 2026, prior to this arXiv submission: https://zenodo.org/records/21911604
