The gravity dual of Rényi entropy.
The gravity dual of Rényi entropy.
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DOI：
10.1038/ncomms12472
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发表时间：
2016-08-12
影响因子：
16.6
通讯作者：
Dong X
中科院分区：
文献类型：
--
作者：
Dong X
黑洞的一个显著而神秘的性质是它们的熵与视界面积成正比。这个面积定律启发了全息原理，后来在规范-引力对偶性中得到了具体的实现。在这种情况下，纠缠熵是由对偶时空中最小曲面的面积给出的。然而，对面积定律的讨论一直局限于纠缠熵，而对量子态的全面理解需要雷尼熵。在这里，我们证明了所有的雷尼熵都满足全息理论中类似的面积定律，并由对偶宇宙膜的面积给出。这种几何处方是纠缠熵最小表面处方的单参数推广。应用这一点，我们提供了第一个全息计算的相互之间的Rényi信息的任意尺寸的两个磁盘。我们的结果提供了一个框架，有效地研究Rényi熵和理解纠缠结构的强耦合系统和量子引力。黑洞的熵是由视界面积给出的这一发现启发了全息原理，并导致了规范引力对偶性。在这里，作者证明了所有的雷尼熵都满足全息理论中类似的面积定律，并由对偶宇宙膜的面积给出。
A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Rényi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Rényi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Rényi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity. The discovery that the entropy of black holes is given by their horizon area inspired the holographic principle and led to gauge-gravity duality. Here, the author shows that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes.