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arXiv:2009.13493 · Journal of High Energy Physics

Hayden-Preskill decoding from noisy Hawking radiation

Ning Bao, Yuta Kikuchi

Published Feb 1, 2021• 20 citations
arXivHTMLPDF

Abstract

Abstract 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. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.

DOI
10.1007/jhep02(2021)017

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Abstract 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. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.
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. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.
We study the Hayden-Preskill thought experiment at finite temperature and obtain the decoupling condition that the information thrown into an old black hole can be extracted by decoding the Hawking radiation. We then consider the decoding Hayden-Preskill protocol at finite temperature assuming the observer outside the black hole who has the access to the full radiation and the unitary dynamics of the black hole. We also consider the cases when the Hawking radiation has noise and decoherence in the storage. The decoding probabilities and the corresponding fidelities are calculated. It is shown that for all the three cases we have considered, the decoding fidelities are less than unity in general. This result indicates that at finite temperature, the decoding strategy and the recovery algorithm are harder to realize than that at infinite temperature.
We studied the Hayden-Preskill thought experiment with the local projective measurement. Compared to the original model, the measurement is applied on the Hawking radiation that was emitted after throwing the quantum diary into the black hole. Within this setup, we explored various aspects of this model, including the information recovery from the black hole, the relation to the black hole final state proposal, the relation between the Yoshida-Kitaev protocol and Petz recovery map, the effects of the decoherence, and the quantum simulations of the decoding protocols. These aspects may provide us new insights into the non-perturbative nature of quantum black holes.
We present two particular decoding procedures for reconstructing a quantum state from the Hawking radiation in the Hayden-Preskill thought experiment. We work in an idealized setting and represent the black hole and its entangled partner by nnn EPR pairs. The first procedure teleports the state thrown into the black hole to an outside observer by post-selecting on the condition that a sufficient number of EPR pairs remain undisturbed. The probability of this favorable event scales as 1/dA21/d_{A}^21/dA2​, where dAd_AdA​ is the Hilbert space dimension for the input state. The second procedure is deterministic and combines the previous idea with Grover's search. The decoding complexity is O(dAC)\mathcal{O}(d_{A}\mathcal{C})O(dA​C) where C\mathcal{C}C is the size of the quantum circuit implementing the unitary evolution operator UUU of the black hole. As with the original (non-constructive) decoding scheme, our algorithms utilize scrambling, where the decay of out-of-time-order correlators (OTOCs) guarantees faithful state recovery.
We studied the Hayden-Preskill thought experiment with the local projective measurement. Compared to the original model, the measurement is applied to the Hawking radiation that was emitted after throwing the quantum diary into the black hole. Within this setup, we explored the information recovery from the black hole utilizing the Yoshida-Kitaev probabilistic strategy and demonstrated a perfect decoding in the ideal case. Additionally, we analyzed the decoherence effects from the environment on the decoding protocol. It shows that errors represented by the depolarizing channel can reduce the decoding probability and fidelity, while errors represented by the dephasing channel do not affect the decoding protocol. Furthermore, we discussed various aspects of the current model, including its relation to the black hole final state proposal and the quantum simulations of the decoding protocols. Especially, employing the graphical representations, we provide an intuitive derivation of the equivalence between the Yoshida-Kitaev protocol and Petz recovery map.
The non-isometric holographic model of the black hole interior stands out as a potential resolution of the long-standing black hole information puzzle since it remedies the friction between the effective calculation and the microscopic description. In this study, combining the final-state projection model, the non-isometric model of black hole interior and Hayden-Preskill thought experiment, we investigate the information recovery from decoding Hawking radiation and demonstrate the emergence of the Page time in this setup. We incorporate the effective modes into the scrambling inside the horizon, which are usually disregarded in Hayden-Preskill protocols, and show that the Page time can be identified as the transition of information transmission channels from the EPR projection to the local projections. This offers a new perspective on the Page time. We compute the decoupling condition under which retrieving information is feasible and show that this model computes the black hole entropy consistent with the quantum extremal surface calculation. Assuming the full knowledge of the dynamics of the black hole interior, we show how Yoshida-Kitaev decoding strategy can be employed in the modified Hayden-Preskill protocol. Furthermore, we perform experimental tests of both probabilistic and Grover's search decoding strategies on the 7-qubit IBM quantum processors to validate our analytical findings and confirm the feasibility of retrieving information in the non-isometric model. This study would stimulate more interests to explore black hole information problem on the quantum processors.