论文标题
观察性熵，粗量子状态和PETZ恢复：信息理论特性和边界
Observational entropy, coarse quantum states, and Petz recovery: information-theoretic properties and bounds
论文作者
论文摘要
观察性熵提供了量子熵的一般概念，该概念在Boltzmann和Gibbs的熵之间进行了适当的插值，并且最近被认为是提供过度平衡的热力学熵的有用度量。在这里，我们从信息理论的角度研究了观察性熵的数学特性，利用了最近加强的量子相对熵的单调性能的形式。我们介绍了一般应用的观察熵以及与顺序和后处理测量有关的界限和身份的新界限。这项工作中的核心作用是通过我们所谓的``粗粒剂''状态发挥的，``粗粒''状态从测量的统计数据中通过贝叶斯的改编出现，而没有假定对``真实''基本状态的任何知识所在。这种粗粒状状态与真实（但通常不可观察）之间的区分性程度可在观测和冯·诺伊曼熵之间的差异上提供上限和下限。
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ``coarse-grained'' state, which emerges from the measurement's statistics by Bayesian retrodiction, without presuming any knowledge about the ``true'' underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies.
