The gravity dual of Rényi entropy

Dong, Xi

doi:10.1038/ncomms12472

Title: The gravity dual of Rényi entropy

Abstract

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.

Authors:

^[1]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: Fri Aug 12 00:00:00 EDT 2016

Research Org.:: Princeton Univ., NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1358548

Grant/Contract Number:: SC0009988

Resource Type:: Accepted Manuscript

Journal Name:: Nature Communications

Additional Journal Information:: Journal Volume: 7; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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                    Dong, Xi. The gravity dual of Rényi entropy.  United States: N. p., 2016. 
Web.  doi:10.1038/ncomms12472.

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                    Dong, Xi. The gravity dual of Rényi entropy.  United States.  https://doi.org/10.1038/ncomms12472

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                    Dong, Xi. Fri .  
"The gravity dual of Rényi entropy".  United States.  https://doi.org/10.1038/ncomms12472.  https://www.osti.gov/servlets/purl/1358548.

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@article{osti_1358548,

  title        = {The gravity dual of Rényi entropy},

  author       = {Dong, Xi},

  abstractNote = {A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.},

  doi          = {10.1038/ncomms12472},

  journal      = {Nature Communications},

  number       = ,

  volume       = 7,

  place        = {United States},

  year         = {Fri Aug 12 00:00:00 EDT 2016},

  month        = {Fri Aug 12 00:00:00 EDT 2016}

}

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Holographic Renyi Entropy from Quantum Error Correction
text, January 2018

Akers, Chris; Rath, Pratik
arXiv
DOI: 10.48550/arxiv.1811.05171

Flat entanglement spectra in fixed-area states of quantum gravity
text, January 2018

Dong, Xi; Harlow, Daniel; Marolf, Donald
arXiv
DOI: 10.48550/arxiv.1811.05382

Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
text, January 2018

Bao, Ning; Penington, Geoffrey; Sorce, Jonathan
arXiv
DOI: 10.48550/arxiv.1812.01171

De Sitter Space and Entanglement
text, January 2019

Arias, Cesar; Diaz, Felipe; Sundell, Per
arXiv
DOI: 10.48550/arxiv.1901.04554

Quantum vs. classical information: operator negativity as a probe of scrambling
text, January 2019

Kudler-Flam, Jonah; Nozaki, Masahiro; Ryu, Shinsei
arXiv
DOI: 10.48550/arxiv.1906.07639

Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
text, January 2019

Anastasiou, Giorgos; Araya, Ignacio J.; Guijosa, Alberto
arXiv
DOI: 10.48550/arxiv.1908.11447

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Title: The gravity dual of Rényi entropy

Abstract

Citation Formats

The four laws of black hole mechanics journal, June 1973

Particle creation by black holes journal, August 1975

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

The large $N$ limit of superconformal field theories and supergravity journal, January 1998

Gauge theory correlators from non-critical string theory journal, May 1998

Anti de Sitter space and holography journal, January 1998

Towards a derivation of holographic entanglement entropy journal, May 2011

Generalized gravitational entropy journal, August 2013

Holographic entanglement entropy for general higher derivative gravity journal, January 2014

Generalized entropy and higher derivative gravity journal, March 2014

Quantum corrections to holographic entanglement entropy journal, November 2013

Measuring entanglement entropy in a quantum many-body system journal, December 2015

Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations journal, April 2010

Holographic duality from random tensor networks journal, November 2016

Rényi entropies for free field theories journal, April 2012

Geometric and renormalized entropy in conformal field theory journal, August 1994

Rényi entropies of free bosons on the torus and holography journal, April 2014

Comments on Rényi entropy in AdS3/CFT2 journal, May 2014

Virasoro conformal blocks in closed form journal, August 2015

Rényi entropies, the analytic bootstrap, and 3D quantum gravity at higher genus journal, July 2015

A universal feature of CFT Rényi entropy journal, March 2014

Twist operators in higher dimensions journal, October 2014

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

Rényi entropy and conformal defects journal, July 2016

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories journal, June 2016

Holographic calculations of Rényi entropy journal, December 2011

Entanglement Rényi entropies in conformal field theories and holography journal, May 2012

Holographic Rényi entropies at finite coupling journal, August 2013

Holographic phases of Rényi entropies journal, December 2013

Holographic Rényi entropy for CFT with W symmetry journal, April 2014

Holographic charged Rényi entropies journal, December 2013

Supersymmetric Rényi entropy journal, October 2013

The holographic supersymmetric Rényi entropy in five dimensions journal, February 2015

Supersymmetric Renyi entropy in CFT 2 and AdS 3 journal, January 2016

Entropy and area journal, August 1993

Colloquium : Area laws for the entanglement entropy journal, February 2010

Thermodynamics of Chaotic Systems journal, January 2009

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime journal, January 2015

A covariant holographic entanglement entropy proposal journal, July 2007

Topological aspects of generalized gravitational entropy journal, May 2015

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

The world as a hologram journal, November 1995

Thermodynamics of Spacetime: The Einstein Equation of State journal, August 1995

Building up spacetime with quantum entanglement journal, June 2010

Cool horizons for entangled black holes journal, August 2013

Holographic GB gravity in arbitrary dimensions journal, March 2010

Rényi entropy and conformal defects text, January 2016

The large N limit of superconformal field theories and supergravity conference, January 1999

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Holographic GB gravity in arbitrary dimensions text, January 2009

Towards a derivation of holographic entanglement entropy text, January 2011

Generalized gravitational entropy text, January 2013

Cool horizons for entangled black holes text, January 2013

Supersymmetric Renyi Entropy text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Holographic Entanglement Entropy for General Higher Derivative Gravity text, January 2013

Holographic Reconstruction of General Bulk Surfaces text, January 2014

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime text, January 2014

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity text, January 2014

Topological aspects of generalized gravitational entropy text, January 2014

Virasoro conformal blocks in closed form text, January 2015

Holographic duality from random tensor networks text, January 2016

Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories text, January 2016

Thermodynamics of Spacetime: The Einstein Equation of State text, January 1995

The World as a Hologram text, January 1994

The Large N Limit of Superconformal Field Theories and Supergravity text, January 1997

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

Universality in the geometric dependence of Rényi entropy journal, January 2015

Geometric and renormalized entropy in conformal field theory journal, August 1994

Rényi entropy and geometry journal, June 2014

Rényi entropy and conformal defects text, January 2016

Quantum corrections to holographic entanglement entropy text, January 2013

Renyi entropy, stationarity, and entanglement of the conformal scalar text, January 2014

The holographic supersymmetric Renyi entropy in five dimensions text, January 2014

Supersymmetric Renyi Entropy in $CFT_2$ and $AdS_3$ text, January 2015

Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories text, January 2016

The four laws of black hole mechanics
journal, June 1973

Particle creation by black holes
journal, August 1975

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

The large $N$ limit of superconformal field theories and supergravity
journal, January 1998

Gauge theory correlators from non-critical string theory
journal, May 1998

Anti de Sitter space and holography
journal, January 1998

Towards a derivation of holographic entanglement entropy
journal, May 2011

Generalized gravitational entropy
journal, August 2013

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Generalized entropy and higher derivative gravity
journal, March 2014

Quantum corrections to holographic entanglement entropy
journal, November 2013

Measuring entanglement entropy in a quantum many-body system
journal, December 2015

Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations
journal, April 2010

Holographic duality from random tensor networks
journal, November 2016

Rényi entropies for free field theories
journal, April 2012

Geometric and renormalized entropy in conformal field theory
journal, August 1994

Rényi entropies of free bosons on the torus and holography
journal, April 2014

Comments on Rényi entropy in AdS3/CFT2
journal, May 2014

Virasoro conformal blocks in closed form
journal, August 2015

Rényi entropies, the analytic bootstrap, and 3D quantum gravity at higher genus
journal, July 2015

A universal feature of CFT Rényi entropy
journal, March 2014

Twist operators in higher dimensions
journal, October 2014

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

Rényi entropy and conformal defects
journal, July 2016

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories
journal, June 2016

Holographic calculations of Rényi entropy
journal, December 2011

Entanglement Rényi entropies in conformal field theories and holography
journal, May 2012

Holographic Rényi entropies at finite coupling
journal, August 2013

Holographic phases of Rényi entropies
journal, December 2013

Holographic Rényi entropy for CFT with W symmetry
journal, April 2014

Holographic charged Rényi entropies
journal, December 2013

Supersymmetric Rényi entropy
journal, October 2013

The holographic supersymmetric Rényi entropy in five dimensions
journal, February 2015

Supersymmetric Renyi entropy in CFT 2 and AdS 3
journal, January 2016

Entropy and area
journal, August 1993

Colloquium : Area laws for the entanglement entropy
journal, February 2010

Thermodynamics of Chaotic Systems
journal, January 2009

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015

A covariant holographic entanglement entropy proposal
journal, July 2007

Topological aspects of generalized gravitational entropy
journal, May 2015

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

The world as a hologram
journal, November 1995

Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995

Building up spacetime with quantum entanglement
journal, June 2010

Cool horizons for entangled black holes
journal, August 2013

Holographic GB gravity in arbitrary dimensions
journal, March 2010

Rényi entropy and conformal defects
text, January 2016

The large N limit of superconformal field theories and supergravity
conference, January 1999

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Holographic GB gravity in arbitrary dimensions
text, January 2009

Towards a derivation of holographic entanglement entropy
text, January 2011

Generalized gravitational entropy
text, January 2013

Cool horizons for entangled black holes
text, January 2013

Supersymmetric Renyi Entropy
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Holographic Entanglement Entropy for General Higher Derivative Gravity
text, January 2013

Holographic Reconstruction of General Bulk Surfaces
text, January 2014

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
text, January 2014

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
text, January 2014

Topological aspects of generalized gravitational entropy
text, January 2014

Virasoro conformal blocks in closed form
text, January 2015

Holographic duality from random tensor networks
text, January 2016

Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
text, January 2016

Thermodynamics of Spacetime: The Einstein Equation of State
text, January 1995

The World as a Hologram
text, January 1994

The Large N Limit of Superconformal Field Theories and Supergravity
text, January 1997

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

Universality in the geometric dependence of Rényi entropy
journal, January 2015

Geometric and renormalized entropy in conformal field theory
journal, August 1994

Rényi entropy and geometry
journal, June 2014

Rényi entropy and conformal defects
text, January 2016

Quantum corrections to holographic entanglement entropy
text, January 2013

Renyi entropy, stationarity, and entanglement of the conformal scalar
text, January 2014

The holographic supersymmetric Renyi entropy in five dimensions
text, January 2014

Supersymmetric Renyi Entropy in $CFT_2$ and $AdS_3$
text, January 2015

Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
text, January 2016

The Holographic Entropy Arrangement
journal, February 2019

Note on ETH of descendant states in 2D CFT
journal, January 2019

Expanding the black hole interior: partially entangled thermal states in SYK
journal, February 2019