Quantum Extremal Surfaces and the Holographic Entropy Cone
Quantum Extremal Surfaces and the Holographic Entropy Cone
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DOI：
10.1007/jhep11(2021)177
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发表时间：
2021-08
影响因子：
5.4
通讯作者：
C. Akers;Sergio Hernandez-Cuenca;Pratik Rath
中科院分区：
文献类型：
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作者：
C. Akers;Sergio Hernandez-Cuenca;Pratik Rath
已知具有几何熵的量子态满足比一般量子系统更严格的熵不等式。使用Ryu-Takayanagi（RT）公式导出的允许熵集定义了全息熵锥（HEC）。这些不等式不再满足，一旦一般的量子修正包括采用量子极值曲面（QES）处方。然而，QES公式的结构允许控制研究如何从批量熵的量子贡献与HEC不等式的相互作用。在本文中，我们开始探索这个问题的相关散装熵约束边界熵不等式。特别是，我们表明，需要大量熵满足HEC意味着边界熵也满足HEC。此外，我们还表明，要求大量熵服从一夫一妻的互信息（MMI）意味着边界熵也服从MMI。
Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.