Locality of Gravitational Systems from Entanglement of Conformal Field Theories.
Locality of Gravitational Systems from Entanglement of Conformal Field Theories.
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DOI：
10.1103/physrevlett.114.221601
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发表时间：
2015-06
影响因子：
8.6
通讯作者：
Jennifer Lin;M. Marcolli;H. Ooguri;Bogdan Stoica
中科院分区：
文献类型：
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作者：
Jennifer Lin;M. Marcolli;H. Ooguri;Bogdan Stoica
Ryu-Takayanagi公式将共形场理论中的纠缠熵与其全息对偶中最小表面的面积联系起来。我们证明了这一关系可以在共形场论中对任何状态进行倒转，以计算体时空边界附近的体应力-能量张量，从边界上的纠缠重构体中的局部数据。我们还证明了保形场论中任意态的约简密度矩阵与基态的约简密度矩阵之间的小球面上相对熵的正性、单调性和凸性是由体物质能量密度的正条件保证的。由于相对熵的正性和单调性是量子系统的一般性质，这可以解释为任何全息系统中适用Ryu-Takayanagi处方的体能条件的推导。我们讨论了在费雪度规方面的凸性的信息理论解释。
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.