Bit threads and holographic entanglement of purification

Harper, Jonathan; Headrick, Matthew

doi:10.1007/JHEP08(2019)101

Title: Bit threads and holographic entanglement of purification

Abstract

Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite case we find the flows exhibit novel behavior which allows for a constrained flux on the boundary of the homology region. We show this flux can be made distinct from bi-partite terms and reflects the truly multipartite portion of the holographic entanglement of purification.

Authors:

^[1]; Headrick, Matthew ^[1]

Brandeis Univ., Waltham, MA (United States)

Publication Date:: Tue Aug 20 00:00:00 EDT 2019

Research Org.:: Brandeis Univ., Waltham, MA (United States)

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

OSTI Identifier:: 1595095

Report Number(s):: arXiv:1906.05970v3
Journal ID: ISSN 1029-8479; TRN: US2101747

Grant/Contract Number:: SC0009987; 1068620

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: 8; 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; Differential and Algebraic Geometry

Citation Formats


                    Harper, Jonathan, and Headrick, Matthew. Bit threads and holographic entanglement of purification.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP08(2019)101.

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                    Harper, Jonathan, & Headrick, Matthew. Bit threads and holographic entanglement of purification.  United States.  https://doi.org/10.1007/JHEP08(2019)101

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                    Harper, Jonathan, and Headrick, Matthew. Tue .  
"Bit threads and holographic entanglement of purification".  United States.  https://doi.org/10.1007/JHEP08(2019)101.  https://www.osti.gov/servlets/purl/1595095.

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@article{osti_1595095,

  title        = {Bit threads and holographic entanglement of purification},

  author       = {Harper, Jonathan and Headrick, Matthew},

  abstractNote = {Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite case we find the flows exhibit novel behavior which allows for a constrained flux on the boundary of the homology region. We show this flux can be made distinct from bi-partite terms and reflects the truly multipartite portion of the holographic entanglement of purification.},

  doi          = {10.1007/JHEP08(2019)101},

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

  number       = 8,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Aug 20 00:00:00 EDT 2019},

  month        = {Tue Aug 20 00:00:00 EDT 2019}

}

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Works referenced in this record:

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Umemoto, Koji; Zhou, Yang
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Title: Bit threads and holographic entanglement of purification

Abstract

Citation Formats

Entanglement of purification for multipartite states and its holographic dual journal, October 2018

Entanglement of purification in free scalar field theories journal, April 2018

Convex Optimization book, January 2004

Entanglement of purification: from spin chains to holography journal, January 2018

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

Monogamy, polygamy, and other properties of entanglement of purification journal, April 2015

Entanglement of purification through holographic duality journal, March 2018

The entanglement of purification journal, September 2002

A covariant holographic entanglement entropy proposal journal, July 2007

Surface/state correspondence as a generalized holography journal, July 2015

Riemannian and Lorentzian flow-cut theorems journal, April 2018

Aspects of holographic entanglement entropy journal, August 2006

Entanglement of purification and multiboundary wormhole geometries journal, February 2019

Bit Threads and Holographic Entanglement journal, November 2016

Holographic inequalities and entanglement of purification journal, March 2018

Entanglement of Purification in Many Body Systems and Symmetry Breaking journal, May 2019

Entanglement Wedge Cross Section from the Dual Density Matrix journal, April 2019

Holographic Entanglement of Purification from Conformal Field Theories journal, March 2019

General properties of holographic entanglement entropy journal, March 2014

Geometric aspects of holographic bit threads journal, May 2019

“Squashed entanglement”: An additive entanglement measure journal, March 2004

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Surface/State Correspondence as a Generalized Holography text, January 2015

Entanglement of purification: from spin chains to holography text, January 2017

Entanglement of Purification in Free Scalar Field Theories text, January 2018

Aspects of Holographic Entanglement Entropy text, January 2006

The entanglement of purification text, January 2002

Entanglement of purification for multipartite states and its holographic dual
journal, October 2018

Entanglement of purification in free scalar field theories
journal, April 2018

Convex Optimization
book, January 2004

Entanglement of purification: from spin chains to holography
journal, January 2018

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

Monogamy, polygamy, and other properties of entanglement of purification
journal, April 2015

Entanglement of purification through holographic duality
journal, March 2018

The entanglement of purification
journal, September 2002

A covariant holographic entanglement entropy proposal
journal, July 2007

Surface/state correspondence as a generalized holography
journal, July 2015

Riemannian and Lorentzian flow-cut theorems
journal, April 2018

Aspects of holographic entanglement entropy
journal, August 2006

Entanglement of purification and multiboundary wormhole geometries
journal, February 2019

Bit Threads and Holographic Entanglement
journal, November 2016

Holographic inequalities and entanglement of purification
journal, March 2018

Entanglement of Purification in Many Body Systems and Symmetry Breaking
journal, May 2019

Entanglement Wedge Cross Section from the Dual Density Matrix
journal, April 2019

Holographic Entanglement of Purification from Conformal Field Theories
journal, March 2019

General properties of holographic entanglement entropy
journal, March 2014

Geometric aspects of holographic bit threads
journal, May 2019

“Squashed entanglement”: An additive entanglement measure
journal, March 2004

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Surface/State Correspondence as a Generalized Holography
text, January 2015

Entanglement of purification: from spin chains to holography
text, January 2017

Entanglement of Purification in Free Scalar Field Theories
text, January 2018

Aspects of Holographic Entanglement Entropy
text, January 2006

The entanglement of purification
text, January 2002