In the Hayden-Preskill thought experiment, the Hawking radiation emitted before a quantum state is thrown into the black hole is used along with the radiation collected later for the purpose of decoding the quantum state. A natural question is how the recoverability is affected if the stored early radiation is damaged or subject to decoherence, and/or the decoding protocol is imperfectly performed. In the first part, I talk about the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation. In the second part, I present an application of the Hayden-Preskill protocol, that is used to quantify how scrambled a given quantum system is. It has advantage over the direct measurement of out-of-time ordered correlators when used to diagnose the information scrambling in the presence of the noise effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory.
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