自由费米子黑洞作为偏振镜

中文摘要 AI 辅助

理解各类量子系统能够以多快的速度扰乱信息，是量子信息理论的一个关键目标，既关乎基础物理学，也关乎量子算法效率的研究。众所周知，这种理解使海登和普雷斯基尔得以证明，在黑洞动力学可由哈达姆随机酉算子建模的假设下，老年黑洞充当“镜子”，将落入的量子信息几乎瞬时地反射出来。在本工作中，我们通过考虑一个随机的自由费米子黑洞动力学模型，研究这种镜像行为在超出哈达姆随机设定后有哪些方面得以保留。我们发现，信息释放的速率由底层的表示论结构所决定；这样的黑洞表现为一面“偏振镜”，保留编码在低费米子阶不可约表示中的信息，同时以快得多的速度反射编码在高费米子阶不可约表示中的信息。由于低阶信息的保留，我们证明，除非黑洞已蒸发到仅剩一个可忽略的极小部分，否则无法忠实地恢复落入的量子信息。然而，用固定的克利福德酉算子增强动力学可以恢复其反射行为，尽管该系综的框架势保持不变，且远高于其哈达姆值。值得注意的是，我们发现此类黑洞可以胜过其完全哈达姆随机的对应物：在高保真度极限下，恢复单量子比特消息所需的发射量子比特数渐近地减少约37%。

英文摘要

Understanding the speed with which various classes of quantum systems can scramble information is a key goal of quantum information theory, with relevance to both fundamental physics and the study of the efficiency of quantum algorithms. Famously, such understanding enabled Hayden and Preskill to show that, under the assumption that black hole dynamics may be modelled by a Haar-random unitary, old black holes act as ''mirrors'', reflecting infalling quantum information back out again effectively instantaneously. In this work, we investigate which aspects of this mirror behaviour survive beyond the Haar-random setting by considering a random free fermionic model of black hole dynamics. We find that the rate of information release is governed by the underlying representation-theoretic structure; such a black hole acts as a ''polarised mirror'', retaining information encoded in low fermionic-degree irreps while reflecting information encoded in high fermionic-degree irreps much more rapidly. As a result of the retention of low-degree information, we show that faithful recovery of the infalling quantum information is impossible until all but a vanishing fraction of the black hole has evaporated. However, augmenting the dynamics with a fixed Clifford unitary can restore their reflective behaviour, even though the ensemble's frame potential remains unchanged and far above its Haar value. Remarkably, we find that such black holes can outperform their fully Haar-random counterparts: in the high-fidelity limit, recovering a single-qubit message requires asymptotically approximately $37\%$ fewer emitted qubits.

发表机构

• University of Melbourne（墨尔本大学）
• Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
• Quantum Science Center（量子科学中心）

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