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 leading order than the minimal QES), toge...
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Format: | Article |
Language: | English |
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SpringerOpen
2021-04-01
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Series: | Journal of High Energy Physics |
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Online Access: | https://doi.org/10.1007/JHEP04(2021)062 |
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author | Chris Akers Geoff Penington |
author_facet | Chris Akers Geoff Penington |
author_sort | Chris Akers |
collection | DOAJ |
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 | 2024-12-22T05:40:32Z |
format | Article |
id | doaj.art-519214ba43924f6ba182064913faaa6b |
institution | Directory Open Access Journal |
issn | 1029-8479 |
language | English |
last_indexed | 2024-12-22T05:40:32Z |
publishDate | 2021-04-01 |
publisher | SpringerOpen |
record_format | Article |
series | Journal of High Energy Physics |
spelling | doaj.art-519214ba43924f6ba182064913faaa6b2022-12-21T18:37:11ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021417310.1007/JHEP04(2021)062Leading order corrections to the quantum extremal surface prescriptionChris Akers0Geoff Penington1Center for Theoretical Physics, Massachusetts Institute of TechnologyCenter for Theoretical Physics, University of CaliforniaAbstract 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.https://doi.org/10.1007/JHEP04(2021)062AdS-CFT CorrespondenceNonperturbative EffectsGauge-gravity correspondence |
spellingShingle | Chris Akers Geoff Penington Leading order corrections to the quantum extremal surface prescription Journal of High Energy Physics AdS-CFT Correspondence Nonperturbative Effects Gauge-gravity correspondence |
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 |
topic | AdS-CFT Correspondence Nonperturbative Effects Gauge-gravity correspondence |
url | https://doi.org/10.1007/JHEP04(2021)062 |
work_keys_str_mv | AT chrisakers leadingordercorrectionstothequantumextremalsurfaceprescription AT geoffpenington leadingordercorrectionstothequantumextremalsurfaceprescription |