论文标题
Ke li的引理量子假设检验在一般的von Neumann代数中
Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras
论文作者
论文摘要
ke li在[arxiv：1208.1400]中陈述的引理已在例如[Arxiv：1510.04682，Arxiv：1706.04590，Arxiv：1612.01464，ARXIV：1308.6503，ARXIV：1602.08898]对于量子假设测试，具有量子侧侧信息或量子信息分布的各种任务。该引理最初在有限的尺寸中被证明，直接扩展到I型Von Neumann代数。在这里，我们表明，模块化理论的使用允许为引理构建的对象提供更透明的含义，并证明了对一般的von Neumann代数。这产生了量子Stein的引理的新证明，其假设略有较弱，并且立即概括了其二阶渐近学，例如[Arxiv：1510.04682]和[Arxiv：1208.1400]的主要结果。
A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. This lemma was originally proven in finite dimension, with a direct extension to type I von Neumann algebras. Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras. This yields a new proof of quantum Stein's lemma with slightly weaker assumption, as well as immediate generalizations of its second order asymptotics, for example the main results in [arXiv:1510.04682] and [arXiv:1208.1400].
