Flat entanglement spectra in fixed-area states of quantum gravity

Dong, Xi; Harlow, Daniel; Marolf, Donald

doi:10.1007/jhep10(2019)240

Title: Flat entanglement spectra in fixed-area states of quantum gravity

Abstract

We use the Einstein-Hilbert gravitational path integral to investigate gravitational entanglement at leading order O(1/G). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies Sn are independent of n at this order. The n-dependence of Sn in more general states then arises from sums over the RT/HRT-area, which are generally dominated by different values of this area for each n. This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of algebraic centers which arise in the quantum errorcorrecting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh.

Authors:

^[1]; Harlow, Daniel ^[2]; Marolf, Donald ^[1]

Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

Publication Date:: Thu Oct 24 00:00:00 EDT 2019

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1803476

Grant/Contract Number:: SC0018944; SC0019127

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: 2019; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Dong, Xi, Harlow, Daniel, and Marolf, Donald. Flat entanglement spectra in fixed-area states of quantum gravity.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep10(2019)240.

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                    Dong, Xi, Harlow, Daniel, & Marolf, Donald. Flat entanglement spectra in fixed-area states of quantum gravity.  United States.  https://doi.org/10.1007/jhep10(2019)240

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                    Dong, Xi, Harlow, Daniel, and Marolf, Donald. Thu .  
"Flat entanglement spectra in fixed-area states of quantum gravity".  United States.  https://doi.org/10.1007/jhep10(2019)240.  https://www.osti.gov/servlets/purl/1803476.

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@article{osti_1803476,

  title        = {Flat entanglement spectra in fixed-area states of quantum gravity},

  author       = {Dong, Xi and Harlow, Daniel and Marolf, Donald},

  abstractNote = {We use the Einstein-Hilbert gravitational path integral to investigate gravitational entanglement at leading order O(1/G). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies Sn are independent of n at this order. The n-dependence of Sn in more general states then arises from sums over the RT/HRT-area, which are generally dominated by different values of this area for each n. This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of algebraic centers which arise in the quantum errorcorrecting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh.},

  doi          = {10.1007/jhep10(2019)240},

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

  number       = 10,

  volume       = 2019,

  place        = {United States},

  year         = {Thu Oct 24 00:00:00 EDT 2019},

  month        = {Thu Oct 24 00:00:00 EDT 2019}

}

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The holographic dual of the entanglement wedge symplectic form
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Title: Flat entanglement spectra in fixed-area states of quantum gravity

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Relative entropy equals bulk relative entropy journal, June 2016

Entropy, extremality, euclidean variations, and the equations of motion journal, January 2018

Gravitational splitting at first order: Quantum information localization in gravity journal, October 2018

Decomposition of entanglement entropy in lattice gauge theory journal, April 2012

Deriving covariant holographic entanglement text, January 2016

A universal feature of CFT Rényi entropy journal, March 2014

Hot multiboundary wormholes from bipartite entanglement text, January 2015

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

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Aspects of entanglement entropy for gauge theories journal, January 2016

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

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Cool horizons for entangled black holes journal, August 2013

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

Discrete gravity on random tensor network and holographic Rényi entropy journal, November 2017

Deriving covariant holographic entanglement journal, November 2016

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Local Quantum Physics book, January 1992

Diffeomorphism invariant actions for partial systems journal, April 1995

On the Architecture of Spacetime Geometry preprint, January 2012

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

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Holographic Renyi entropy from quantum error correction journal, May 2019

Entropy and area journal, August 1993

Bulk locality from modular flow journal, July 2017

Living on the edge: a toy model for holographic reconstruction of algebras with centers journal, April 2017

Dynamical origin of the entropy of a black hole journal, November 1993

Generalized gravitational entropy journal, August 2013

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence journal, June 2015

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

Local phase space and edge modes for diffeomorphism-invariant theories journal, February 2018

Remarks on entanglement entropy for gauge fields journal, April 2014

Quantum corrections to holographic entanglement entropy journal, November 2013

Hot multiboundary wormholes from bipartite entanglement journal, October 2015

Proof of the holographic formula for entanglement entropy journal, September 2006

Entanglement renormalization and holography journal, September 2012

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

Proof of the holographic formula for entanglement entropy journal, September 2006

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Deriving covariant holographic entanglement text, January 2016

Bulk locality from modular flow text, January 2017

The holographic dual of the entanglement wedge symplectic form text, January 2020

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Building up spacetime with quantum entanglement
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Holographic Rényi Entropy at High Energy Density
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Multiboundary wormholes and holographic entanglement
journal, September 2014

Eternal black holes in anti-de Sitter
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The gravity dual of Rényi entropy
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Local subsystems in gauge theory and gravity
journal, September 2016

On the architecture of spacetime geometry
journal, October 2014

Microcanonical path integrals and the holography of small black hole interiors
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Entanglement Rényi entropies in holographic theories
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Cool horizons for entangled black holes
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Local quantum physics
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On the entanglement entropy for gauge theories
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Holographic Entanglement Entropy for General Higher Derivative Gravity
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Holographic duality from random tensor networks
journal, November 2016

Bit Threads and Holographic Entanglement
journal, November 2016

How is quantum information localized in gravity?
journal, October 2017

Local Quantum Physics
book, January 1996

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

Generalized gravitational entropy
text, January 2013

Holographic Renyi Entropy from Quantum Error Correction
text, January 2018

Multiboundary Wormholes and Holographic Entanglement
text, January 2014

A covariant holographic entanglement entropy proposal
journal, July 2007

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

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

Local phase space and edge modes for diffeomorphism-invariant theories
text, January 2017

Generalized entropy and higher derivative gravity
journal, March 2014

Distinguishability of black hole microstates
journal, September 2017

Aspects of holographic entanglement entropy
journal, August 2006

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

Relative entropy equals bulk relative entropy
journal, June 2016

Entropy, extremality, euclidean variations, and the equations of motion
journal, January 2018

Gravitational splitting at first order: Quantum information localization in gravity
journal, October 2018

Decomposition of entanglement entropy in lattice gauge theory
journal, April 2012

Deriving covariant holographic entanglement
text, January 2016

A universal feature of CFT Rényi entropy
journal, March 2014

Hot multiboundary wormholes from bipartite entanglement
text, January 2015

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

Holographic duality from random tensor networks
text, January 2016

Aspects of entanglement entropy for gauge theories
journal, January 2016

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

Quantum corrections to holographic entanglement entropy
text, January 2013

Cool horizons for entangled black holes
journal, August 2013

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

Discrete gravity on random tensor network and holographic Rényi entropy
journal, November 2017

Deriving covariant holographic entanglement
journal, November 2016

TASI Lectures on the Emergence of Bulk Physics in AdS/CFT
conference, September 2018

Local Quantum Physics
book, January 1992

Diffeomorphism invariant actions for partial systems
journal, April 1995

On the Architecture of Spacetime Geometry
preprint, January 2012

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

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Holographic Renyi entropy from quantum error correction
journal, May 2019

Entropy and area
journal, August 1993

Bulk locality from modular flow
journal, July 2017

Living on the edge: a toy model for holographic reconstruction of algebras with centers
journal, April 2017

Dynamical origin of the entropy of a black hole
journal, November 1993

Generalized gravitational entropy
journal, August 2013

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

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

Local phase space and edge modes for diffeomorphism-invariant theories
journal, February 2018

Remarks on entanglement entropy for gauge fields
journal, April 2014

Quantum corrections to holographic entanglement entropy
journal, November 2013

Hot multiboundary wormholes from bipartite entanglement
journal, October 2015

Proof of the holographic formula for entanglement entropy
journal, September 2006

Entanglement renormalization and holography
journal, September 2012

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

Proof of the holographic formula for entanglement entropy
journal, September 2006

Quantum corrections to holographic entanglement entropy
text, January 2013

Deriving covariant holographic entanglement
text, January 2016

Bulk locality from modular flow
text, January 2017

The holographic dual of the entanglement wedge symplectic form
text, January 2020

The holographic dual of the entanglement wedge symplectic form
text, January 2020

The holographic dual of the entanglement wedge symplectic form
journal, January 2020

The Holographic Dual of the Entanglement Wedge Symplectic Form
text, January 2019