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.
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.
Quantum information is scrambled via a chaotic time evolution in many-body systems. Clarifying how and to what extent we can recover the quantum information from the scrambled state is a central issue of today's physics, since it commonly appears as an essential factor in various topics including irreversibility of quantum chaotic dynamics, fault-tolerant quantum computation, and black hole information paradox. In realistic settings, symmetry can ubiquitously exist in scrambling dynamics. Here we establish fundamental limitations on the information recovery arising from the Lie group symmetries in the scrambling dynamics. The results are applicable to many situations, including the Hayden-Preskill black hole model with symmetry where the success rate of the information recovery qualitatively changes from the original no-symmetry case. Our findings show a close relationship between information recovery, symmetry, and quantum coherence, and that symmetry hinders the quantum information recovery.
In this paper, we consider the time evolution of entanglement asymmetry of the black hole radiation in the Hayden-Preskill thought experiment. We assume the black hole is initially in a mixed state since it is entangled with the early radiation. Alice throws a diary maximally entangled with a reference system into the black hole. After the black hole has absorbed the diary, Bob tries to recover the information that Alice thought should be destroyed by the black hole. In this protocol, we found that a U ( 1 ) symmetry of the radiation emerges before a certain transition time (the time when the vanishing entanglement asymmetry begins to grow). This emergent symmetry is exact in the thermodynamic limit and can be characterized by the vanishing entanglement asymmetry of the radiation. The transition time depends on the initial entropy and the size of the diary. What is more, when the initial state of the black hole is maximally mixed, this emergent symmetry survives during the whole procedure of the black hole radiation. We successfully explained this novel phenomenon using the decoupling inequality.
Quantum information is scrambled via chaotic time evolution in many-body systems. The recovery of initial information embedded locally in the system from the scrambled quantum state is a fundamental concern in many contexts. From a dynamical perspective, information recovery can measure dynamical instability in quantum chaos, fault-tolerant quantum computing, and the black hole information paradox. This article considers general aspects of quantum information recovery when the scrambling dynamics have conservation laws due to Lie group symmetries. Here, we establish fundamental limitations on the information recovery from scrambling dynamics with arbitrary Lie group symmetries. We show universal relations between information recovery, symmetry, and quantum coherence, which apply to many physical situations. The relations predict that the behavior of the Hayden-Preskill black hole model changes qualitatively under the assumption of the energy conservation law. Consequently, we can rigorously prove that under the energy conservation law, the error of the information recovery from a small black hole remains unignorably large until it completely evaporates. Moreover, even when the black hole is very large, the recovery of information thrown into the black hole is not completed until most of the black hole evaporates. The relations also provide a unified view of the symmetry restrictions on quantum information processing, such as the approximate Eastin-Knill theorem and the Wigner-Araki-Yanase theorem for unitary gates.
We construct the Hayden-Preskill protocol by using a system of spin-1/2 particles and demonstrate information flows of this system which can mimic black holes. We first define an analogous black hole A as a collection of such particles. Second, we take the particles from inside to outside the black hole to define an analogous system of Hawking radiation B as outside particles. When the black hole and the radiation have the maximum entanglement at the Page time, we take an entangled pair system C and D. The particles of C fall into the black hole while their counterparts of D remain outside. If we assume rapid mixing of the particle states in the black hole A ⋃ C , can the information of C rapidly escape from the black hole like a mirror? We numerically show that if we turn on the rapid mixing in the black hole, the original information of C rapidly escapes from the black hole to outside in the form of the mutual information between B and D. On the other hand, if the mixing between A and C is not enough, the information escapes slowly. Hence, we explicitly demonstrate the original conjecture of Hayden and Preskill. We emphasize that enough mixing is an essential condition to make the Hayden-Preskill protocol functionally work.
Hayden and Preskill proposed a thought experiment in which Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and for which Yoshida and Kitaev recently proposed a concrete decoding scheme.In the context of quantum many-body physics, the parallel question is that after a small system is thermalized with a large system, how can one decode the initial state information with the help of two entangled many-body systems?Here, we propose to realize this decoding protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state.We show that the Yoshida-Kitaev protocol allows us to read out the initial spin information after it is scrambled into the cavity.We show that the readout efficiency reaches a maximum when the model parameters are tuned to the regime where the system is the most chaotic, characterized by the shortest scrambling time in the out-of-time-ordered correlation function.Our proposal opens up the possibility of discussing this profound thought experiment in a realistic setting.
We review and analyse quantum information-theoretic approaches to black hole evaporation that purport to bring us closer to a resolution of the black hole information paradox. Our focus is on the Page-time paradox and on the contribution of the Hayden-Preskill model to understanding information release under the assumption of unitary evaporation. In this model, the black hole is taken to be a finite-dimensional quantum system whose dynamics can be represented by a quantum circuit, and its information-processing and communication abilities are studied. We identify the assumptions underlying this modelling and highlight two key features, fast scrambling dynamics and entanglement as a resource, that underpin the information release in the model. We argue that this reasoning exemplifies a broader change in how information is used in black hole physics, in which quantum information theory now provides a useful operational modelling framework. This application avoids earlier philosophical objections insofar as it is not based on epistemic ignorance and does not regard information as a substance. This line of reasoning has become central to the debate and, as such, warrants greater attention from the philosophy of physics community.