The ghost in the radiation: robust encodings of the black hole interior
Open accessAbstract
A bstract: 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.
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In all cases, inherent chaos in microstate dynamics should connect the Python's lunch geometric mechanism of generating exponential complexity in encoding with the pseudorandomness mechanism.
“In all cases, the inher-ent chaos in microstate dynamics should connect the Python's lunch geometric mechanism of generating exponential complexity [236] in encoding with the pseudorandomness mechanism discussed in [258].”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [258]
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The entropy of Hawking radiation
Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., & Tajdini, A. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.035002 · Cited by 706 · see citing works
“The actual quantum operations we would need to perform on the radiation are expected to be exceedingly complex, with a complexity that is (roughly) exponential in the black hole entropy [21,79].”
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Chen, H. Z., Fisher, Z., Hernandez, J., Myers, R. C., & Ruan, S.-M. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)065 · Cited by 99 · see citing works
Holographic spacetime, black holes and quantum error correcting codes: a review
Kibe, T., Mandayam, P., & Mukhopadhyay, A. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10382-1 · Cited by 44 · see citing works
“should connect the Python’s lunch geometric mechanism of generating exponential complexity [228] in encoding with the pseudorandomness mechanism discussed in [249].”
Background
- Authors
- Kim, I., Tang, E., & Preskill, J.
- Affiliations
- The University of Sydney (AU)
- California Institute of Technology (US)
- Corresponding author
- Kim, Isaac
- Venue
- Journal of High Energy Physics
- Published
- 2020-06-03
- Volume
- 2020
- Issue
- 6
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W3011148986
- Cited by
- 63
- References
- 14
- Citations by year
- 2026: 4 · 2025: 11 · 2024: 8 · 2023: 10 · 2022: 5 · 2021: 13 · 2020: 12
- FWCI
- 4.42
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1733907)
- U.S. Department of Energy (DESC0018407)
- Simons Foundation
- Institute for Quantum Information and Matter, California Institute of Technology (PHY-1733907)
- Natural Sciences and Engineering Research Council of Canada (PHY-1733907)
- Australian Research Council (CE170100009)
- Air Force Office of Scientific Research (FA9550-, FA9550-19- 1-0360)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- black hole firewalls, black hole interior, Hawking radiation, quantum error correction, quantum computational complexity, pseudorandomness, black hole complementarity, entanglement, quantum memory, black hole entropy
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