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.

中文翻译：

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有限温度下的 BROTOC 和量子信息加扰

近年来，无序相关器 (OTOC) 作为量子信息加扰的诊断方法得到了广泛的研究。在本文中，我们研究了正则化有限温度 OTOC 的量子信息理论方面。我们介绍了二分正则化 OTOC (BROTOC) 的分析结果：正则化 OTOC 在二分支持的随机单一元上平均。我们展示了 BROTOC 有几个有趣的特性，例如，它量化了相关热场双态的纯度和分析持续时间演化算子的​​算子纯度。在无限温度下，它减少到一减去时间演化算子的​​算子纠缠。在零温度极限和非简并哈密顿量下，BROTOC 探测基态纠缠。通过计算长期平均值，我们表明 BROTOC 的平衡值与本征态纠缠密切相关。最后，我们对各种物理相关哈密顿模型的 BROTOC 平衡值进行了数值研究，并评论了其区分可积和混沌动力学的能力。