arXiv 1710.033632017-10-16hep-thquant-ph

Hayden-Preskill协议的高效译码

Efficient decoding for the Hayden-Preskill protocol

Beni Yoshida, Alexei Kitaev

备注：: 17 pages, 3 figures

摘要：

本文介绍了在Hayden-Preskill思想实验中从霍金辐射重建量子态的两种特殊解码方法。我们在一个理想化的设置和代表黑洞和它的纠缠伙伴的$n$ EPR对。第一个程序的条件下，有足够数量的EPR对保持不受干扰的后选择的状态被扔到黑洞到外部观察者的心灵传输。该有利事件的概率按比例缩放为$1/d_{A}^2$，其中$d_A$是输入状态的希尔伯特空间维度。第二个过程是确定性的，并结合了前面的想法与Grover的搜索。解码复杂度是$\mathcal{O}(d_{A}\mathcal{C})$，其中$\mathcal{C}$是实现黑洞的酉演化算子$U$的量子线路的大小。与原始的（非建设性的）解码方案，我们的算法利用加扰，其中的衰减的时间顺序（OTOC）保证忠实的状态恢复。

英文摘要：

We present two particular decoding procedures for reconstructing a quantum state from the Hawking radiation in the Hayden-Preskill thought experiment. We work in an idealized setting and represent the black hole and its entangled partner by $n$ EPR pairs. The first procedure teleports the state thrown into the black hole to an outside observer by post-selecting on the condition that a sufficient number of EPR pairs remain undisturbed. The probability of this favorable event scales as $1/d_{A}^2$, where $d_A$ is the Hilbert space dimension for the input state. The second procedure is deterministic and combines the previous idea with Grover's search. The decoding complexity is $\mathcal{O}(d_{A}\mathcal{C})$ where $\mathcal{C}$ is the size of the quantum circuit implementing the unitary evolution operator $U$ of the black hole. As with the original (non-constructive) decoding scheme, our algorithms utilize scrambling, where the decay of out-of-time-order correlators (OTOCs) guarantees faithful state recovery.

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摘要：

英文摘要：

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