Black hole entanglement and quantum error correction
Black hole entanglement and quantum error correction
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DOI：
10.1007/jhep10(2013)107
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发表时间：
2012-11
影响因子：
5.4
通讯作者：
E. Verlinde;H. Verlinde
中科院分区：
文献类型：
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作者：
E. Verlinde;H. Verlinde
最近[1]中有人提出，黑洞互补性对量子信息论的基本规则造成了压力，例如纠缠的一夫一妻制。受这一论点的启发，我们开发了一个实用的框架，通过单一时间演化来描述黑洞蒸发，该框架基于全息视角，其中所有黑洞自由度都存在于延伸的地平线上。我们将视界建模为具有有限熵的酉量子系统，并且不假设视界几何形状是平滑的。然后我们证明，通过温和的假设，人们可以重建探测黑洞内部的局域有效场论可观测量，相对于视界附近的状态看起来像局域闵可夫斯基真空。重建利用了量子纠错码的形式，适用于纠缠熵尚未饱和贝肯斯坦-霍金界的黑洞态。我们的总体框架阐明了黑洞最终状态的提议，并允许对向最大混合黑洞状态的“防火墙”状态的过渡进行定量研究。
It was recently argued in [1] that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and do not postulate that the horizon geometry is smooth. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state proposal, and allows a quantitative study of the transition into the “firewall” regime of maximally mixed black hole states.