Abstract
Hayden and Preskill proposed a thought experiment that Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and Yoshida and Kitaev recently proposed a concrete decoding scheme. The parallel question is that after a small system is thermalized with a large system, how one can decode the initial state information with the help of two entangled many-body systems. Here we propose to realize this 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 parameter is 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.
Highlights
Quantum information scrambling plays an important role in understanding quantum many-body systems
When a many-body system evolving from an initial state thermalizes, all the local information about the initial state gets lost, since a thermalized many-body system is described by only a few parameters such as temperature and chemical potential [1,2,3,4]
When Alice throws her diary into the black hole, Bob cannot recover the information in the diary from the Hawking radiation, which is just a small portion of the entire Hilbert space of a black hole
Summary
Quantum information scrambling plays an important role in understanding quantum many-body systems. The local information of the initial state has been scrambled into the entire system during the process of quantum thermalization, such that the retrieval of this local information from local measurements is not possible [5,6] This information loss is reminiscent of the black hole information problem. Yoshida and Kitaev (YK) went a step forward and described a procedure for realizing the HP protocol [15] Their protocol requires the evolution of the quantum system described by a Haar random unitary evolution [16], which perfectly scrambles the information as a black hole. They require that the unitary evolutions of two entangled many-body systems are conjugates of each other [15]. The purpose of this paper is to investigate how all these practical effects influence the efficiency of the YKHP protocol
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