发表机构
Scuola Normale Superiore; The Chinese University of Hong Kong, Shenzhen; International Quantum Academy (SIQA); Nagoya University（比萨高等师范学院; 香港中文大学（深圳）; 国际量子学院; 名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将广义量子Stein引理推广到更一般的源，即渐近接近i.i.d.的态，并据此求解了任意变化零假设下的Stein指数，简化了理论并扩展了应用范围。
AI 中文摘要
广义量子Stein引理是量子假设检验中的一个关键结果，它将量子信息处理这一基本原语与量子资源操控联系起来，而后者对于技术应用至关重要。先前的工作已在独立同分布（i.i.d.）量子态序列的理想化背景下证明了该陈述，近期的扩展还考虑了根据Mazzola、Sutter和Renner提出的严格定义，与i.i.d.‘接近’的源。然而，对于若干应用，需要考虑更一般的源。我们建立了一个概念上更简单且更一般的广义量子Stein引理版本，因为它适用于任何在归一化量子Wasserstein距离（阶数为1）意义下渐近接近i.i.d.态的源。作为直接推论，我们解决了零假设任意变化场景下的Stein指数，将其表示为对应于零假设基础集凸包中任意态的i.i.d. Stein指数。
英文摘要
The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.
Comments66 pages, 7 figures
