Distinguishing Random and Black Hole Microstates
Distinguishing Random and Black Hole Microstates
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DOI：
10.1103/prxquantum.2.040340
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发表时间：
2021-07
期刊：
影响因子：
9.7
通讯作者：
Jonah Kudler-Flam;Vladimir Narovlansky;S. Ryu
中科院分区：
文献类型：
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作者：
Jonah Kudler-Flam;Vladimir Narovlansky;S. Ryu
这是简短报告[物理学]的扩充版。其中，相对熵被用于区分从Wishart系综中提取的随机状态以及黑洞微观状态。在这项工作中，我们通过计算许多概括来扩展这些想法，包括Petz r横梁相对熵、三明治r横梁相对熵、保真度和跟踪距离。这些广义量能够告诉我们随机状态和黑洞微观状态空间中的新结构，在这些空间中，冯·诺伊曼和相对熵是不够的。我们进一步推广到一般随机张量网络，其中由于网络中的局部性产生了新的现象。这些现象强化了全息状态和随机张量网络之间的关系。我们讨论了我们的结果对使用复制虫洞的黑洞信息问题的影响，特别是霍金辐射中的状态依赖（毛发）。理解不同蒸发黑洞的霍金辐射之间的差异是信息问题的一个重要部分，而使用孤岛公式的熵计算并没有解决这个问题。我们用量子假设检验和子系统特征态热化假设（ETH）的语言解释了我们的结果，推导出混沌（包括全息）系统在小于总系统尺寸一半的所有子系统中都服从子系统ETH。ar X iv:2 10 8。00 01 1v 1 [p] 3 0 Ju 1 2 02 1
This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603 (2021)], where the relative entropy was used to distinguish random states drawn from the Wishart ensemble as well as black hole microstates. In this work, we expand these ideas by computing many generalizations including the Petz Rényi relative entropy, sandwiched Rényi relative entropy, fidelities, and trace distances. These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient. We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks. These phenomena sharpen the relationship between holographic states and random tensor networks. We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation. Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula. We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size. ar X iv :2 10 8. 00 01 1v 1 [ he pth ] 3 0 Ju l 2 02 1