The Hayden-Preskill protocol probes the capability of information recovery from local subsystems after unitary dynamics. As such it resolves the capability of quantum many-body systems to dynamically implement a quantum error-correcting code. The transition to coding behavior has been mostly discussed using effective approaches, such as entanglement membrane theory. Here, we present exact results on the use of Hayden-Preskill recovery as a dynamical probe of scrambling in local quantum many-body systems. We investigate certain classes of unitary circuit models, both structured Floquet (dual-unitary) and Haar-random circuits. We discuss different dynamical signatures corresponding to information transport or scrambling, respectively, that go beyond effective approaches. Surprisingly, certain chaotic circuits transport information with perfect fidelity. In integrable dual-unitary circuits, we relate the information transmission to the propagation and scattering of quasiparticles. Using numerical and analytical insights, we argue that the qualitative features of information recovery extend away from these solvable points. Our results suggest that information recovery protocols can serve to distinguish chaotic and integrable behavior, and that they are sensitive to characteristic dynamical features, such as long-lived quasiparticles or dual-unitarity.

中文翻译：

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混沌可积酉电路动力学中的 Hayden-Preskill 恢复


Hayden-Preskill 协议探讨了单一动力学后从本地子系统恢复信息的能力。因此，它解决了量子多体系统动态实现量子纠错码的能力。向编码行为的转变主要是使用有效的方法来讨论的，例如纠缠膜理论。在这里，我们展示了使用 Hayden-Preskill 恢复作为局部量子多体系统中扰乱的动态探针的精确结果。我们研究了某些类别的酉电路模型，包括结构化 Floquet（双酉）电路和 Haar 随机电路。我们分别讨论了与信息传输或加扰相对应的不同动态签名，这些签名超出了有效的方法。令人惊讶的是，某些混沌电路以完美的保真度传输信息。在可积双酉电路中，我们将信息传输与准粒子的传播和散射联系起来。利用数值和分析见解，我们认为信息恢复的定性特征远离了这些可解点。我们的结果表明，信息恢复协议可以用于区分混沌和可积行为，并且它们对特征动力学特征敏感，例如长寿命准粒子或对偶幺正性。