发表机构
Scuola Normale Superiore（高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明全局pretty good measurement的误差概率至多为二元最优误差之和的四倍，并构造正则单纯形系综证明该系数最优，改进了现有成对界，提供了更简单的矩阵分析证明及单次Chernoff界。
AI 中文摘要
我们确定了从多重量子假设检验到二元量子假设检验约化中的最优普适系数。具体而言，对于任意希尔伯特空间维度（有限或无限）中的每个有限系综，我们证明了全局pretty good measurement（PGM）的误差概率至多是二元最优误差概率之和的四倍。通过构造一族正则单纯形系综，我们进一步证明即使对于任意全局测量，系数四也是最优的。这一结果改进了Cheng和Liu [arXiv:2606.06246 (2026)]建立的成对界，并为标准PGM本身提供了明确的、尖锐的保证。我们的证明也更简单：我们不是构造序贯测量并应用联合界，而是纯粹依赖矩阵分析技术，结合PGM误差的直接块Gram矩阵分析和量子Hellinger距离与Bures $\chi^2$-散度之间的精细不等式。我们的分析还产生了精细的单次成对Chernoff界以及达到期望判别误差所需的显式副本数。
英文摘要
We determine the optimal universal coefficient in a reduction of multiple to binary quantum hypothesis testing. Specifically, for every finite ensemble in any Hilbert space dimension (finite or infinite), we prove that the error probability of the global pretty good measurement (PGM) is at most four times the sum of the optimal binary error probabilities. By constructing a family of regular-simplex ensembles, we further show that the coefficient four is optimal, even for arbitrary global measurements. This result improves on the pairwise bounds established by Cheng and Liu [arXiv:2606.06246 (2026)] and entails an explicit, sharp guarantee for the standard PGM itself. Our proof is also simpler: rather than constructing sequential measurements and applying a union bound, our proof relies on purely matrix-analytic techniques, combining a direct block Gram matrix analysis of the PGM error and a refined inequality between quantum Hellinger distance and Bures $χ^2$-divergence. Our analysis also yields a refined, one-shot pairwise Chernoff bound and explicit sufficient number of copies for a desired discrimination error.
Comments11 pages
