Linearity of holographic entanglement entropy

Almheiri, Ahmed; Dong, Xi; Swingle, Brian

doi:10.1007/JHEP02(2017)074

Title: Linearity of holographic entanglement entropy

Abstract

Here, we consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.

Authors:

Almheiri, Ahmed ^[1]; Dong, Xi ^[2]; Swingle, Brian ^[1]

Stanford Univ., CA (United States). Inst. for Theoretical Physics, Dept. of Physics
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: Tue Feb 14 00:00:00 EST 2017

Research Org.:: Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

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

OSTI Identifier:: 1358372

Alternate Identifier(s):: OSTI ID: 1356081

Grant/Contract Number:: SC0009988; PHY-1316699

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: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; Black Holes in String Theory; Gauge-gravity correspondence; Conformal Field Theory; level-spacing distributions; black-holes; airy kernel; quantum; system; states; AdS-CFT correspondence; black holes in string theory; gauge-gravity correspondence; conformal field theory

Citation Formats


                    Almheiri, Ahmed, Dong, Xi, and Swingle, Brian. Linearity of holographic entanglement entropy.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP02(2017)074.

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                    Almheiri, Ahmed, Dong, Xi, & Swingle, Brian. Linearity of holographic entanglement entropy.  United States.  https://doi.org/10.1007/JHEP02(2017)074

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                    Almheiri, Ahmed, Dong, Xi, and Swingle, Brian. Tue .  
"Linearity of holographic entanglement entropy".  United States.  https://doi.org/10.1007/JHEP02(2017)074.  https://www.osti.gov/servlets/purl/1358372.

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@article{osti_1358372,

  title        = {Linearity of holographic entanglement entropy},

  author       = {Almheiri, Ahmed and Dong, Xi and Swingle, Brian},

  abstractNote = {Here, we consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.},

  doi          = {10.1007/JHEP02(2017)074},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 2,

  volume       = 2017,

  place        = {United States},

  year         = {Tue Feb 14 00:00:00 EST 2017},

  month        = {Tue Feb 14 00:00:00 EST 2017}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

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Journal of Mathematical Physics, Vol. 59, Issue 3
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journal, May 2017

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Communications in Mathematical Physics, Vol. 354, Issue 3
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Universal local operator quenches and entanglement entropy
journal, November 2019

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Journal of High Energy Physics, Vol. 2019, Issue 11
DOI: 10.1007/jhep11(2019)107

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Toward a Holographic Theory for General Spacetimes
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Title: Linearity of holographic entanglement entropy

Abstract

Citation Formats

The Spectra of Quantum States and the Kronecker Coefficients of the Symmetric Group journal, October 2005

Symmetry properties of product states for the system of N n ‐level atoms journal, May 1988

Level-spacing distributions and the Airy kernel journal, May 1993

ER=EPR, GHZ, and the consistency of quantum measurements: ER=EPR, GHZ, and the consistency of quantum measurements journal, January 2016

Estimating the spectrum of a density operator journal, October 2001

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

A covariant holographic entanglement entropy proposal journal, July 2007

Quantum state transformations and the Schubert calculus journal, January 2005

Gravitational Radiation from Colliding Black Holes journal, May 1971

Eternal black holes and superselection in AdS/CFT journal, December 2012

The Pauli Principle Revisited journal, July 2008

Cool horizons for entangled black holes journal, August 2013

Gaussian Quantum Marginal Problem journal, February 2008

Comments on microcausality, chaos, and gravitational observables journal, November 2015

Thermal fluctuations in quantized chaotic systems journal, February 1996

Stabilizer information inequalities from phase space distributions journal, August 2013

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

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

Generalized gravitational entropy journal, August 2013

Quantum corrections to holographic entanglement entropy journal, November 2013

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

The gravity duals of modular Hamiltonians journal, September 2016

Extremal surface barriers journal, March 2014

Quantum Theory of Gravity. I. The Canonical Theory journal, August 1967

Construction of bulk fields with gauge redundancy journal, September 2012

Causality & holographic entanglement entropy journal, December 2014

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

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality journal, July 2016

Bulk and transhorizon measurements in AdS/CFT journal, October 2012

Quantum statistical mechanics in a closed system journal, February 1991

Thermodynamics of black holes in anti-de Sitter space journal, December 1983

Moulting Black Holes journal, March 2012

Level-spacing distributions and the Airy kernel journal, January 1994

Holographic entanglement entropy from 2d CFT: heavy states and local quenches journal, February 2015

AdS3 holography for 1/4 and 1/8 BPS geometries journal, November 2015

Universality of long-distance AdS physics from the CFT bootstrap journal, August 2014

Entanglement of Superpositions journal, September 2006

Black holes: complementarity or firewalls? journal, February 2013

An apologia for firewalls journal, September 2013

Local Operators in the Eternal Black Hole journal, November 2015

Black holes and the butterfly effect journal, March 2014

Multiple shocks journal, December 2014

Quantum universal variable-length source coding journal, August 2002

The holographic entropy cone journal, September 2015

Semiclassical Wheeler wormhole production journal, March 1991

Entropy in black hole pair production journal, January 1994

The information theoretic interpretation of the length of a curve journal, June 2015

Quantum Theory of Gravity. I. The Canonicál Theory journal, July 1968

Estimating the Spectrum of a Density Operator book, February 2005

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Moulting Black Holes text, January 2011

Bulk and Transhorizon Measurements in AdS/CFT text, January 2012

Eternal Black Holes and Superselection in AdS/CFT text, January 2012

Generalized gravitational entropy text, January 2013

Cool horizons for entangled black holes text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Extremal Surface Barriers text, January 2013

Universality of Long-Distance AdS Physics from the CFT Bootstrap text, January 2014

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

Causality & holographic entanglement entropy text, January 2014

The Gravity Duals of Modular Hamiltonians preprint, January 2014

Local Operators in the Eternal Black Hole text, January 2015

AdS3 Holography for 1/4 and 1/8 BPS geometries text, January 2015

Comments on Microcausality, Chaos, and Gravitational Observables text, January 2015

Entropy in Black Hole Pair Production text, January 1993

Level-Spacing Distributions and the Airy Kernel text, January 1992

Quantum universal variable-length source coding text, January 2002

Quantum state transformations and the Schubert calculus text, January 2004

Detecting topology change via correlations and entanglement from gauge/gravity correspondence journal, March 2018

The Ryu–Takayanagi Formula from Quantum Error Correction journal, May 2017

Universal local operator quenches and entanglement entropy journal, November 2019

The Ryu-Takayanagi Formula from Quantum Error Correction text, January 2016

Toward a Holographic Theory for General Spacetimes text, January 2016

Holographic Renyi Entropy from Quantum Error Correction text, January 2018

Universal Local Operator Quenches and Entanglement Entropy text, January 2019

The Spectra of Quantum States and the Kronecker Coefficients of the Symmetric Group
journal, October 2005

Symmetry properties of product states for the system of N n ‐level atoms
journal, May 1988

Level-spacing distributions and the Airy kernel
journal, May 1993

ER=EPR, GHZ, and the consistency of quantum measurements: ER=EPR, GHZ, and the consistency of quantum measurements
journal, January 2016

Estimating the spectrum of a density operator
journal, October 2001

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

A covariant holographic entanglement entropy proposal
journal, July 2007

Quantum state transformations and the Schubert calculus
journal, January 2005

Gravitational Radiation from Colliding Black Holes
journal, May 1971

Eternal black holes and superselection in AdS/CFT
journal, December 2012

The Pauli Principle Revisited
journal, July 2008

Cool horizons for entangled black holes
journal, August 2013

Gaussian Quantum Marginal Problem
journal, February 2008

Comments on microcausality, chaos, and gravitational observables
journal, November 2015

Thermal fluctuations in quantized chaotic systems
journal, February 1996

Stabilizer information inequalities from phase space distributions
journal, August 2013

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

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

Generalized gravitational entropy
journal, August 2013

Quantum corrections to holographic entanglement entropy
journal, November 2013

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

The gravity duals of modular Hamiltonians
journal, September 2016

Extremal surface barriers
journal, March 2014

Quantum Theory of Gravity. I. The Canonical Theory
journal, August 1967

Construction of bulk fields with gauge redundancy
journal, September 2012

Causality & holographic entanglement entropy
journal, December 2014

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

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
journal, July 2016

Bulk and transhorizon measurements in AdS/CFT
journal, October 2012

Quantum statistical mechanics in a closed system
journal, February 1991

Thermodynamics of black holes in anti-de Sitter space
journal, December 1983

Moulting Black Holes
journal, March 2012

Level-spacing distributions and the Airy kernel
journal, January 1994

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

AdS3 holography for 1/4 and 1/8 BPS geometries
journal, November 2015

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

Entanglement of Superpositions
journal, September 2006

Black holes: complementarity or firewalls?
journal, February 2013

An apologia for firewalls
journal, September 2013

Local Operators in the Eternal Black Hole
journal, November 2015

Black holes and the butterfly effect
journal, March 2014

Multiple shocks
journal, December 2014

Quantum universal variable-length source coding
journal, August 2002

The holographic entropy cone
journal, September 2015

Semiclassical Wheeler wormhole production
journal, March 1991

Entropy in black hole pair production
journal, January 1994

The information theoretic interpretation of the length of a curve
journal, June 2015

Quantum Theory of Gravity. I. The Canonicál Theory
journal, July 1968

Estimating the Spectrum of a Density Operator
book, February 2005

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Moulting Black Holes
text, January 2011

Bulk and Transhorizon Measurements in AdS/CFT
text, January 2012

Eternal Black Holes and Superselection in AdS/CFT
text, January 2012

Generalized gravitational entropy
text, January 2013

Cool horizons for entangled black holes
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Extremal Surface Barriers
text, January 2013

Universality of Long-Distance AdS Physics from the CFT Bootstrap
text, January 2014

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

Causality & holographic entanglement entropy
text, January 2014

The Gravity Duals of Modular Hamiltonians
preprint, January 2014

Local Operators in the Eternal Black Hole
text, January 2015

AdS3 Holography for 1/4 and 1/8 BPS geometries
text, January 2015

Comments on Microcausality, Chaos, and Gravitational Observables
text, January 2015

Entropy in Black Hole Pair Production
text, January 1993

Level-Spacing Distributions and the Airy Kernel
text, January 1992

Quantum universal variable-length source coding
text, January 2002

Quantum state transformations and the Schubert calculus
text, January 2004

Detecting topology change via correlations and entanglement from gauge/gravity correspondence
journal, March 2018

The Ryu–Takayanagi Formula from Quantum Error Correction
journal, May 2017

Universal local operator quenches and entanglement entropy
journal, November 2019

The Ryu-Takayanagi Formula from Quantum Error Correction
text, January 2016

Toward a Holographic Theory for General Spacetimes
text, January 2016

Holographic Renyi Entropy from Quantum Error Correction
text, January 2018

Universal Local Operator Quenches and Entanglement Entropy
text, January 2019