论文标题
黑洞内部的量子误差校正
Quantum Error Correction in the Black Hole Interior
论文作者
论文摘要
我们研究玩具模型中黑洞内部的量子误差校正特性，用于蒸发黑洞：jackiw-teitelboim重力与非重力浴室纠结。页面时间之后，该系统中的黑洞内部自由度被编码在Hilbert Space中。我们使用引力路径积分来表明内部密度矩阵可以与量子操作在浴缸上的作用进行纠正，而量子操作的作用（i）没有事先访问黑洞微杆菌的细节，并且（ii）在浴缸上没有黑洞的最大混合状态，并没有黑洞的下限和黑洞的下限，并没有黑洞的最大混合状态，并具有黑洞的下限和代码。因此，辐射中黑洞内部的编码是可靠的，可抵御通用的低级量子操作。对于擦除误差，重力属于$ O（1）$饱和的单例限制的距离校正校正代码的距离。对于浴室中的典型错误以破坏内部，它们必须具有浴希尔伯特空间尺寸的大元素，并具有由黑洞熵和代码子空间维度设置的精确系数。
We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an $O(1)$ distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.
