发表机构
Department of Applied Mathematics and Theoretical Physics, University of Cambridge; School of Mathematics and Statistics, Wuhan University; Department of Mathematical Sciences, Chalmers University of Technology（剑桥大学应用数学与理论物理系; 武汉大学数学与统计学院; 查尔姆斯理工大学数学科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文将条件熵对偶性推广至任意冯·诺依曼代数子代数，并建立无限维量子斯坦引理，为子代数相对熵提供复合假设检验中的操作解释。
AI 中文摘要
我们建立了任意冯·诺依曼代数子代数相对条件熵的对偶关系，涵盖Umegaki相对熵以及夹层和Petz-Rényi散度。即使在有限维情形，这些结果也将条件熵的常见对偶性从张量积子系统推广到一般子代数，同时将框架提升至完全无限维设置。作为应用，当备择假设为有限指标子代数的态空间时，我们建立了量子斯坦引理的无限维推广，这给出了相对熵到子代数的操作解释，即复合量子假设检验中最优渐近误差指数——这是首个超越有限维的结果。
英文摘要
We establish duality relations for conditional entropies relative to subalgebras of arbitrary von Neumann algebras, including the Umegaki relative entropy as well as the sandwiched- and Petz-Rényi divergences. Even in finite dimensions, these results extend the familiar dualities for conditional entropies from tensor-product subsystems to general subalgebras, while also lifting the framework to the fully infinite-dimensional setting. As an application, we establish an infinite-dimensional extension of quantum Stein's lemma when the alternative hypothesis is the state space of a finite-index subalgebra, which gives an operational interpretation of the relative entropy to a subalgebra as the optimal asymptotic error exponent in composite quantum hypothesis testing-the first beyond finite dimensions.
Comments67 pages, no figures
