BROTOCs and Quantum Information Scrambling at Finite Temperature
BROTOCs and Quantum Information Scrambling at Finite Temperature
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DOI：
10.22331/q-2022-06-27-746
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发表时间：
2021-11
期刊：
影响因子：
6.4
通讯作者：
N. Anand;P. Zanardi
中科院分区：
文献类型：
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作者：
N. Anand;P. Zanardi
超时有序相关器(OTOCs)作为量子信息置乱的一种诊断手段，近年来得到了广泛的研究。本文研究了正则化有限温度OTOC的量子信息论问题。我们介绍了二部正则化OTOC(BROTOC)的分析结果：正则化OTOC平均在二分划上的随机么正上。我们发现BROTOC有几个有趣的性质，例如，它量化了相关热场双态的纯度和解析连续的时间演化算符的算符纯度。在无限大的温度下，它减少到1减去时间演化算符的算符纠缠。在零温度极限下，对于非简并哈密顿量，BROTOC探测了基态纠缠。通过计算长时间平均，我们发现BROTOC的平衡值与本征态纠缠密切相关。最后，我们数值研究了各种物理相关的哈密顿模型的BROTOC的平衡值，并评价了它区分可积动力学和混沌动力学的能力。
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.