Michael Rampp, Max Planck Institute for the Physics of Complex Systems

Hayden-Preskill recovery in chaotic and integrable unitary-circuit dynamics

Quantum many-body systems distribute localized information over many non-local degrees of freedom in the course of their time evolution, a process called information scrambling. Information scrambling is related to fundamental questions in quantum dynamics such as thermalization, quantum chaos, and entanglement spreading, and to the control of information dynamics in quantum computing platforms. The Hayden-Preskill protocol probes the capability of information recovery from local subsystems after unitary transformations. It has mostly been discussed for global unitary transformations in the thermodynamic limit without any internal time or length scales. Here, we investigate the use of Hayden-Preskill recovery as a dynamical probe of scrambling in local quantum many-body systems. We present exact results for certain classes of unitary circuit models, both structured (dual-unitary) and Haar-random circuits, and discuss different dynamical signatures corresponding to information transport or scrambling, respectively. Surprisingly, certain chaotic circuits can transport information with perfect fidelity. In integrable dual-unitary circuits, we relate the information transmission to the transport 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 can be used to identify characteristic dynamical features, such as quasiparticles or underlying dual-unitarity.