We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi [J. Math. Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li [Ann. Statist. 44 (2016)] by removing its dimension-dependent prefactor. In the asymptotic many-copy regime, our bound proves the achievability of the multiple quantum Chernoff distance for arbitrary separable Hilbert spaces, thereby settling the previously open infinite-dimensional case, and further yields constant-factor sharp asymptotics for the optimal error probability. In binary quantum hypothesis testing, we prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity. Consequently, the optimal binary quantum error probability is within a factor of two of the optimal classical error probability for the associated Nussbaum-Szkoła distributions, complementing the lower bound of Nussbaum and Szkoła [Ann. Statist. 37 (2009)].

翻译：我们考虑多个量子态之间的贝叶斯判别，并建立了一个无维数的一次性上界，该上界以成对误差之和的形式给出了最小错误概率的界限。这解决了Audenaert和Mosonyi [J. Math. Phys. 55 (2014)] 的猜想，并通过去除其依赖于维度的前置因子，改进了Li [Ann. Statist. 44 (2016)] 的多个量子Chernoff界。在渐近多副本体制下，我们的界证明了任意可分离希尔伯特空间上多个量子Chernoff距离的可达性，从而解决了此前悬而未决的无穷维情形，并进一步给出了最优错误概率的常数因子锐渐近性。在二元量子假设检验中，我们证明最小错误概率可由迹调和平均量表征到通用常数范围内。因此，对于相关的Nussbaum-Szkoła分布，最优二元量子错误概率与最优经典错误概率相差至多两倍，这补充了Nussbaum和Szkola [Ann. Statist. 37 (2009)] 的下界。