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

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.

Ver.1: 7 pages + Supplementary. Ver.2: short version (14 pages) + long version (47 pages). Presentation improved. Connection to thermodynamics is much more elaborated. Ver.3: Substantial update of presentation. 21 pages + 6 pages of appendices. Ver 4-7: improved. Ver 8: Published version

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• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Hayden-Preskill Recovery in Hamiltonian Systems
• Non-Clifford Cost of Random Unitaries
• Decoding general error correcting codes and the role of complementarity
• SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
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• Synthesis of Energy-Conserving Quantum Circuits with XY interaction
• Explicit decoders using fixed-point amplitude amplification based on QSVT