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The ghost in the radiation: robust encodings of the black hole interior (invited paper)

Kim, Isaac H. and Tang, Eugene and Preskill, John (2021) The ghost in the radiation: robust encodings of the black hole interior (invited paper). In: STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ACM , New York, NY, p. 8. ISBN 978-1-4503-8053-9.

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We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Preskill, John0000-0002-2421-4762
Additional Information:© 2021 Copyright held by the owner/author(s).
Funding AgencyGrant Number
Australian Research CouncilCE170100009
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0360
Simons FoundationUNSPECIFIED
Subject Keywords:Quantum Gravity; Black Hole Information; Quantum ErrorCorrecting Code; Quantum Computational Complexity
Record Number:CaltechAUTHORS:20220802-839157000
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Official Citation:Isaac H. Kim, Eugene Tang, and John Preskill. 2021. The Ghost in the Radiation: Robust Encodings of the Black Hole Interior (Invited Paper). In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (STOC ’21), June 21–25, 2021, Virtual, Italy. ACM, New York, NY, USA, 1 page.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116051
Deposited By: George Porter
Deposited On:03 Aug 2022 21:10
Last Modified:03 Aug 2022 21:10

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