Out-of-time-ordered correlators (OTOCs) have been extensively used over the past few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of Styliaris et al. [Phys. Rev. Lett. 126, 030601 (2021)] to the case of open quantum systems. The dynamics is no longer unitary but it is described by more general quantum channels (trace preserving, completely positive maps). This “open bipartite OTOC” can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Moreover, our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence such that the latter can obfuscate the former. To elucidate this subtle interplay, we analytically study special classes of quantum channels, namely, dephasing channels, entanglement-breaking channels, and others. Finally, as a physical application we numerically study dissipative many-body spin chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.

中文翻译：

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开放量子系统中的信息加扰与混沌

在过去几年中，超时间有序相关器 (OTOC) 已被广泛用于研究多体系统中的信息加扰和量子混沌。在本文中，我们扩展了 Styliaris等人的平均二分 OTOC 的形式。[物理。牧师莱特。 126, 030601 (2021)] 以开放量子系统为例。动力学不再是单一的，而是由更一般的量子通道（痕迹保留，完全正映射）描述的。这种“开放的二分 OTOC”可以以精确的分析方式进行处理，并被证明相当于两个量子通道之间的距离。此外，我们的分析形式揭示了来自信息扰乱和环境退相干的竞争熵贡献，使得后者可以混淆前者。为了阐明这种微妙的相互作用，我们分析研究了特殊类别的量子通道，即移相通道、纠缠破坏通道等。最后，