A Caltech Library Service

The ghost in the radiation: robust encodings of the black hole interior

Kim, Isaac and Tang, Eugene and Preskill, John (2020) The ghost in the radiation: robust encodings of the black hole interior. Journal of High Energy Physics, 2020 (6). Art. No. 31. ISSN 1029-8479. doi:10.1007/jhep06(2020)031.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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:Article
Related URLs:
URLURL TypeDescription Paper
Preskill, John0000-0002-2421-4762
Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: March 20, 2020; Accepted: May 13, 2020; Published: June 3, 2020. We thank Adam Bouland, Raphael Bousso, Anne Broadbent, Juan Maldacena, and Geoff Penington for valuable discussions. IK's work was supported by the Simons Foundation It from Qubit Collaboration and by the Australian Research Council via the Centre of Excellence in Engineered Quantum Systems (EQUS) project number CE170100009. Part of this work was done during IK's visit to the Galileo Galilei Institute during the “Entanglement in Quantum Systems” workshop. ET and JP acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907), the Simons Foundation It from Qubit Collaboration, the DOE QuantISED program (DE-SC0018407), and the Air Force Office of Scientific Research (FA9550-19-1-0360). ET acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Australian Research CouncilCE170100009
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0360
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Black Holes, Black Holes in String Theory, AdS-CFT Correspondence
Issue or Number:6
Record Number:CaltechAUTHORS:20200608-102711610
Persistent URL:
Official Citation:Kim, I., Tang, E. & Preskill, J. The ghost in the radiation: robust encodings of the black hole interior. J. High Energ. Phys. 2020, 31 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103744
Deposited By: Tony Diaz
Deposited On:08 Jun 2020 17:36
Last Modified:16 Nov 2021 18:24

Repository Staff Only: item control page