Geometric secret sharing in a model of Hawking radiation
Geometric secret sharing in a model of Hawking radiation
复制标题
DOI：
10.1007/jhep01(2021)177
复制
发表时间：
2020-03
影响因子：
5.4
通讯作者：
V. Balasubramanian;Arjun Kar;Onkar Parrikar;G'abor S'arosi;Tomonori Ugajin
中科院分区：
文献类型：
--
作者：
V. Balasubramanian;Arjun Kar;Onkar Parrikar;G'abor S'arosi;Tomonori Ugajin
我们考虑三维AdS空间中的黑洞与辅助辐射系统纠缠。我们用存在于视界后面世界膜一端的场论来模拟黑洞的微观状态，并允许这个场论本身具有全息对偶几何。这种几何也是一个黑洞，因为微态与辐射的纠缠使它们处于混合态。这个“初始黑洞”可以通过虫洞与辅助系统的纠缠来净化，该辅助系统自然与外部辐射相一致，从而实现ER= EPR场景。在这种情况下，我们提出了一个扩展的Ryu-Takayanagi（RT）公式，其中极值表面计算纠缠熵允许通过膜到其对偶几何。这个新规则再现了蒸发黑洞的Page曲线，与最近提出的“岛公式”一致。然后我们把辐射系统分成几部分。我们的扩展RT规则表明，辐射子系统的联合纠缠楔覆盖黑洞的内部在晚些时候，但子系统的纠缠楔的联合可能不会。这一结果指出了霍金辐射中的秘密共享方案，其中内部某些区域的重建对于辐射的任何子系统都是不可能的，但对于所有子系统都是可能的。
We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER= EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.