[论文解读] Entanglement Wedge Reconstruction and the Information Paradox

Geoffrey Penington|arXiv (Cornell University)|May 20, 2019

Black Holes and Theoretical Physics参考文献 90被引用 44

一句话总结

该论文使用 entanglement wedge 重建与量子 RT 曲面来推导 Page 曲线和 Hayden-Preskill 在蒸发的黑洞中的解码，显示内部信息通过非微扰效应和态相关重建逐步逃逸。

ABSTRACT

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $β/2π\log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

研究动机与目标

• 在 AdS/CFT 框架内通过 entanglement wedge 重建来激发解决黑洞信息悖论的研究。
• Demonstrate a Page-time phase transition of the quantum extremal surface from inside to outside the horizon.
• Show how the Page curve and Hayden-Preskill decoding emerge from holographic entanglement structure.
• Explain state dependence of interior reconstructions and minimal state dependence to avoidFirewalls.

提出的方法

• 采用吸收边界条件和一个辅助辐射储库来建模黑洞蒸发。
• 使用量子极值曲面与广义熵 A/4G_N + S_bulk 来定义 entanglement wedges。
• 在视界内识别一个非空的量子极值曲面，该曲面在 Page 时成为 RT 曲面。
• 通过量子极值曲面跃迁推导 entanglement entropy S = min(S_rad, A_hor/4G_N)。
• 在 entanglement wedge 框架内推广 Hayden-Preskill 至大型 diary 和混合初始态。
• 通过近似算符代数量子纠错和最小态相关界限讨论态相关性。

实验结果

研究问题

• RQ1 蒸发黑洞演化过程中 entanglement wedge 重建如何变化？
• RQ2 是否可以从全息 entanglement 与 RT 曲面推导蒸发黑洞中的 Page 曲线和 Hayden-Preskill 解码标准？
• RQ3 非微扰修正对内部重建和信息逃逸起到什么作用？
• RQ4 不同初始黑洞微态下，态相关性如何影响内部重建？
• RQ5 在蒸发开始前，在最小态相关性下，何种条件可以实现对内部信息的态相关性最小化重建？

主要发现

• 在 Page 时刻发生相变，非空的量子极值曲面成为 RT 曲面，从而产生 Page 曲线。
• CFT 与辐射储库之间的 entanglement entropy S 为 S = min(S_rad, A_hor/4G_N)（至高阶）。
• 内部信息部分编码在早期霍金辐射中，在不放弃半经典体积物理的前提下避免火墙。
• Hayden-Preskill 解码标准源自 entanglement wedge 重建，包括对大型 diary 和未知初始态的推广。
• 内部重建的态相关性会出现但可以被约束；最小态相关性足以避免 AMPSS 火墙悖论。
• 在蒸发前，对于熵小于 Bekenstein-Hawking 熵的码空间，存在与态无关的内部重建；这足以避免典型态导致的火墙。