30 pages. (see posting by M. Piani arXiv:0904.2705 for a different proof of the strict positiveness of the regularized relative entropy of entanglement on every entangled state). published version.
We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties, the most important being the closedness under permutations of the copies. We then determine the error rate function in a very similar fashion to quantum Stein's Lemma, in terms of the quantum relative entropy.
Our result has two applications to entanglement theory. First it gives an operational meaning to an entanglement measure known as regularized relative entropy of entanglement. Second, it shows that this measure is faithful, being strictly positive on every entangled state. This implies, in particular, that whenever a multipartite state can be asymptotically converted into another entangled state by local operations and classical communication, the rate of conversion must be non-zero. Therefore, the operational definition of multipartite entanglement is equivalent to its mathematical definition.
Conditioning on Subalgebras - Entropy Duality and Generalized Quantum Stein's Lemma in von Neumann Algebras
Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；Department of Mathematical Sciences, Chalmers University of Technology（查尔姆斯理工大学数学科学系）
Generalized Stein's lemma and asymptotic equipartition property for subalgebra entropies
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）；Univ Lyon, Inria, ENS Lyon, UCBL, LIP（里昂大学、法国国家信息与自动化研究所、巴黎高等师范学校里昂分校、里昂第一大学、计算机科学实验室）；Wallenberg Centre for Quantum Technology, Chalmers University of Technology（查尔姆斯理工大学瓦伦堡量子技术中心）
Generalised quantum Stein's lemma more robust than ever
Scuola Normale Superiore（比萨高等师范学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；International Quantum Academy (SIQA)（国际量子学院）；Nagoya University（名古屋大学）
Universal quantum resource distillation via composite generalised quantum Stein's lemma
Scuola Normale Superiore（高等师范学校）；Mathematical Quantum Information RIKEN Hakubi Research Team, RIKEN Pioneering Research Institute (PRI) and RIKEN Center for Quantum Computing (RQC)（理研量子信息萩博研究团队、理研先驱研究所（PRI）和理研量子计算中心（RQC））；Department of Basic Science, The University of Tokyo（东京大学基础科学系）
Quantum Channel Stein's Lemma with an Exponential Strong Converse
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras
Ke Li在[arXiv：1208.1400]中陈述的引理已经在例如[arXiv：1510.04682，arXiv：1706.04590，arXiv：1612.01464，arXiv：1308.6503，arXiv：1602.08898]中用于量子假设检验、具有量子边信息的数据压缩或量子密钥分发中的各种任务。这个引理最初是在有限维中证明的，并直接推广到I型冯诺依曼代数。在这里，我们表明，使用模块化理论可以给更透明的意义，构造的引理的对象，并证明它的一般冯诺依曼代数。这就给出了量子Stein引理的一个新的证明，并给出了它的二阶渐近性的直接推广，例如[arXiv：1510.04682]和[arXiv：1208.1400]中的主要结果.
