Complementarity and the unitarity of the black hole S-matrix
A bstract Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S -matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigat...
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Published in | The journal of high energy physics Vol. 2023; no. 2; pp. 233 - 46 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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Abstract | A
bstract
Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole
S
-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the
S
-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the
S
-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the
S
-matrix of an evaporating black hole has polynomial computational complexity. |
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AbstractList | A
bstract
Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole
S
-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the
S
-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the
S
-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the
S
-matrix of an evaporating black hole has polynomial computational complexity. Abstract Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity. Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity. |
ArticleNumber | 233 |
Author | Preskill, John Kim, Isaac H. |
Author_xml | – sequence: 1 givenname: Isaac H. surname: Kim fullname: Kim, Isaac H. email: ikekim@ucdavis.edu organization: Department of Computer Science, UC Davis – sequence: 2 givenname: John surname: Preskill fullname: Preskill, John organization: Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, AWS Center for Quantum Computing |
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Cites_doi | 10.1103/PhysRevD.48.3743 10.1007/JHEP11(2013)074 10.1088/1751-8113/40/28/S18 10.1007/JHEP01(2015)073 10.1088/1126-6708/2007/09/120 10.1103/PhysRevLett.96.181602 10.1103/PhysRevLett.117.120501 10.1103/RevModPhys.93.035002 10.1088/1126-6708/2004/02/008 10.1007/JHEP06(2020)031 10.1103/PRXQuantum.2.040203 10.1103/PhysRevD.84.025007 10.1007/JHEP08(2014)126 10.1007/JHEP06(2013)085 10.1145/3313276.3316366 10.1007/JHEP08(2020)121 10.1098/rspa.2005.1546 10.1088/1126-6708/2004/03/026 10.1007/BF01646490 10.1098/rspa.1985.0070 10.1103/PhysRevLett.106.040403 |
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bstract
Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study... Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of... Abstract Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study... |
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SubjectTerms | Black Holes Classical and Quantum Gravitation Complexity Elementary Particles Entropy High energy physics Holography Models of Quantum Gravity Physics Physics and Astronomy PHYSICS OF ELEMENTARY PARTICLES AND FIELDS Polynomials Principles Pseudorandom Quantum computing Quantum Field Theories Quantum Field Theory Quantum Physics Radiation Regular Article - Theoretical Physics Relativity Theory S matrix theory String Theory |
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Title | Complementarity and the unitarity of the black hole S-matrix |
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