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We study the Hayden-Preskill thought experiment at finite temperature andobtain the decoupling condition that the information thrown into an old blackhole can be extracted by decoding the Hawking radiation. We then consider thedecoding Hayden-Preskill protocol at finite temperature assuming the observeroutside the black hole who has the access to the full radiation and the unitarydynamics of the black hole. We also consider the cases when the Hawkingradiation has noise and decoherence in the storage. The decoding probabilitiesand the corresponding fidelities are calculated. It is shown that for all thethree cases we have considered, the decoding fidelities are less than unity ingeneral. This result indicates that at finite temperature, the decodingstrategy and the recovery algorithm is harder to realize than that at infinitetemperature.

Hayden-Preskill protocol and decoding Hawking radiation at finite temperature