  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.
