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...

Full description

Bibliographic Details
Main Authors: Chris Akers, Geoff Penington
Format: Article
Language:English
Published: SpringerOpen 2021-04-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP04(2021)062
_version_ 1819117913177587712
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