Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics

TL;DR

This paper investigates the Hayden-Preskill recovery protocol in local quantum many-body systems, revealing how information transport and scrambling differ in chaotic versus integrable circuits, and offering exact and numerical insights.

Contribution

It provides exact results and analysis on using Hayden-Preskill recovery to distinguish chaotic and integrable dynamics in quantum circuits, beyond effective theories.

Findings

Chaotic circuits can transmit information with perfect fidelity.

Integrable dual-unitary circuits relate information transfer to quasiparticle dynamics.

Information recovery protocols can differentiate between chaotic and integrable quantum systems.

Abstract

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.