skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Relative entropy equals bulk relative entropy

Abstract

We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

Authors:
 [1];  [2];  [3];  [4]
  1. Harvard Univ., Cambridge, MA (United States). Center for Fundamental Laws of Nature
  2. Princeton Univ., NJ (United States)
  3. Inst. for Advanced Study, Princeton, NJ (United States)
  4. Kavli Inst. for Theoretical Physics, Santa Barbara, CA (United States); Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation
OSTI Identifier:
1327000
Grant/Contract Number:  
SC0009988; PHY-1352084; PHY-1314198; PHY11-25915; 376206
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; 1/N Expansion, Models of Quantum Gravity; Field Theories in Higher Dimensions

Citation Formats

Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, and Suh, S. Josephine. Relative entropy equals bulk relative entropy. United States: N. p., 2016. Web. doi:10.1007/JHEP06(2016)004.
Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, & Suh, S. Josephine. Relative entropy equals bulk relative entropy. United States. doi:10.1007/JHEP06(2016)004.
Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, and Suh, S. Josephine. Wed . "Relative entropy equals bulk relative entropy". United States. doi:10.1007/JHEP06(2016)004. https://www.osti.gov/servlets/purl/1327000.
@article{osti_1327000,
title = {Relative entropy equals bulk relative entropy},
author = {Jafferis, Daniel L. and Lewkowycz, Aitor and Maldacena, Juan and Suh, S. Josephine},
abstractNote = {We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.},
doi = {10.1007/JHEP06(2016)004},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2016,
place = {United States},
year = {2016},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 35 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Relative entropy and the Bekenstein bound
journal, September 2008


Relative entropy and holography
journal, August 2013

  • Blanco, David D.; Casini, Horacio; Hung, Ling-Yan
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)060

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

  • Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)195

Gravitation from entanglement in holographic CFTs
journal, March 2014

  • Faulkner, Thomas; Guica, Monica; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)051

Locality of Gravitational Systems from Entanglement of Conformal Field Theories
journal, June 2015


Inviolable energy conditions from entanglement inequalities
journal, June 2015

  • Lashkari, Nima; Rabideau, Charles; Sabella-Garnier, Philippe
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)067

Canonical energy is quantum Fisher information
journal, April 2016

  • Lashkari, Nima; Van Raamsdonk, Mark
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)153

Towards a derivation of holographic entanglement entropy
journal, May 2011

  • Casini, Horacio; Huerta, Marina; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)036

Entanglement Entropy of Electromagnetic Edge Modes
journal, March 2015


Black hole entropy and entropy of entanglement
journal, October 1995


Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006


A covariant holographic entanglement entropy proposal
journal, July 2007

  • Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2007, Issue 07
  • DOI: 10.1088/1126-6708/2007/07/062

Quantum corrections to holographic entanglement entropy
journal, November 2013

  • Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)074

The four laws of black hole mechanics
journal, June 1973

  • Bardeen, J. M.; Carter, B.; Hawking, S. W.
  • Communications in Mathematical Physics, Vol. 31, Issue 2
  • DOI: 10.1007/BF01645742

Black hole entropy is the Noether charge
journal, October 1993


Some properties of the Noether charge and a proposal for dynamical black hole entropy
journal, July 1994


Rényi entropy, stationarity, and entanglement of the conformal scalar
journal, March 2015

  • Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)075

Stability of Black Holes and Black Branes
journal, December 2012


Reduced density matrix and internal dynamics for multicomponent regions
journal, September 2009


Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

  • Almheiri, Ahmed; Dong, Xi; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)163

The gravity dual of a density matrix
journal, July 2012


Causality & holographic entanglement entropy
journal, December 2014

  • Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)162

Eternal black holes in anti-de Sitter
journal, April 2003


Cool horizons for entangled black holes
journal, August 2013


The off-shell black hole
journal, July 1995


Causal holographic information
journal, June 2012

  • Hubeny, Veronika E.; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2012, Issue 6
  • DOI: 10.1007/JHEP06(2012)114

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014


Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
journal, May 2014


An infalling observer in AdS/CFT
journal, October 2013

  • Papadodimas, Kyriakos; Raju, Suvrat
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)212

Coarse-grained entropy and causal holographic information in AdS/CFT
journal, March 2014


Entanglement Equilibrium and the Einstein Equation
journal, May 2016


Aspects of entanglement entropy for gauge theories
journal, January 2016

  • Soni, Ronak M.; Trivedi, Sandip P.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)136

Black holes: complementarity or firewalls?
journal, February 2013

  • Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)062

An apologia for firewalls
journal, September 2013

  • Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2013, Issue 9
  • DOI: 10.1007/JHEP09(2013)018

Gauge-Gravity Duality and the Black Hole Interior
journal, October 2013


    Works referencing / citing this record:

    Relative entropy for coherent states from Araki formula
    journal, June 2019


    Spectrum of modular Hamiltonian in the vacuum and excited states
    journal, October 2019

    • Das, Suchetan; Ezhuthachan, Bobby
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)009

    Spectrum of modular Hamiltonian in the vacuum and excited states
    journal, October 2019

    • Das, Suchetan; Ezhuthachan, Bobby
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)009

    Relative entropy for coherent states from Araki formula
    journal, June 2019