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The Hayden-Preskill protocol is a qubit-toy model of the black holeinformation paradox. Based on the assumption of scrambling, it was revealedthat quantum information is instantly leaked out from the quantum many-bodysystem that models a black hole. In this paper, we extend the protocol to thecase where the system has symmetry and investigate how the symmetry affects theleakage of information. We especially focus on the conservation of the numberof up-spins. Developing a partial decoupling approach, we first show that thesymmetry induces a delay of leakage and an information remnant. We then clarifythe physics behind them: the delay is characterized by thermodynamic propertiesof the system associated with the symmetry, and the information remnant isclosely related to the symmetry-breaking of the initial state. These relationsbridge the information leakage problem to macroscopic physics of quantummany-body systems and allow us to investigate the information leakage only interms of physical properties of the system.

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