Leading order corrections to the quantum extremal surface prescription
Abstract We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at lea...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/136817 |
| _version_ | 1811093288566915072 |
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| author | Akers, Chris Penington, Geoff |
| author_facet | Akers, Chris Penington, Geoff |
| author_sort | Akers, Chris |
| collection | MIT |
| description | Abstract
We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently. |
| first_indexed | 2024-09-23T15:42:52Z |
| format | Article |
| id | mit-1721.1/136817 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:42:52Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1368172021-11-02T03:05:26Z Leading order corrections to the quantum extremal surface prescription Akers, Chris Penington, Geoff Abstract We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently. 2021-11-01T14:33:34Z 2021-11-01T14:33:34Z 2021-04-08 2021-04-11T03:14:12Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136817 Journal of High Energy Physics. 2021 Apr 08;2021(4):62 PUBLISHER_CC en https://doi.org/10.1007/JHEP04(2021)062 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Akers, Chris Penington, Geoff Leading order corrections to the quantum extremal surface prescription |
| title | Leading order corrections to the quantum extremal surface prescription |
| title_full | Leading order corrections to the quantum extremal surface prescription |
| title_fullStr | Leading order corrections to the quantum extremal surface prescription |
| title_full_unstemmed | Leading order corrections to the quantum extremal surface prescription |
| title_short | Leading order corrections to the quantum extremal surface prescription |
| title_sort | leading order corrections to the quantum extremal surface prescription |
| url | https://hdl.handle.net/1721.1/136817 |
| work_keys_str_mv | AT akerschris leadingordercorrectionstothequantumextremalsurfaceprescription AT peningtongeoff leadingordercorrectionstothequantumextremalsurfaceprescription |