Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry

TL;DR

This paper extends the Hayden-Preskill protocol to systems with symmetry, revealing how symmetry influences information leakage, delay, and remnants, linking quantum information dynamics to thermodynamic and symmetry-breaking properties.

Contribution

It introduces a partial decoupling approach to analyze symmetry effects on information leakage in black hole models, highlighting the role of thermodynamics and symmetry-breaking.

Findings

Symmetry causes a delay in information leakage.

Information remnants are linked to symmetry-breaking.

Leakage dynamics relate to thermodynamic properties.

Abstract

The Hayden-Preskill protocol is a qubit-toy model of the black hole information paradox. Based on the assumption of scrambling, it was revealed that quantum information is instantly leaked out from the quantum many-body system that models a black hole. In this paper, we extend the protocol to the case where the system has symmetry and investigate how the symmetry affects the leakage of information. We especially focus on the conservation of the number of up-spins. Developing a partial decoupling approach, we first show that the symmetry induces a delay of leakage and an information remnant. We then clarify the physics behind them: the delay is characterized by thermodynamic properties of the system associated with the symmetry, and the information remnant is closely related to the symmetry-breaking of the initial state. These relations bridge the information leakage problem to macroscopic physics of quantum many-body systems and allow us to investigate the information leakage only in terms of physical properties of the system.