Multipartite optimized correlation measures and holography

DeWolfe, Oliver; Levin, Joshua; Smith, Graeme

doi:10.1103/PhysRevD.102.066001

Title: Multipartite optimized correlation measures and holography

Abstract

We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced Q correlation and R correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of itsmore » dual.« less

Authors:

DeWolfe, Oliver;

; Smith, Graeme

Publication Date:: 2020-09-08

Research Org.:: Univ. of Colorado, Boulder, CO (United States)

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

OSTI Identifier:: 1658651

Alternate Identifier(s):: OSTI ID: 1714355; OSTI ID: 1762008

Grant/Contract Number:: SC0010005; SC0020386

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 6; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum correlations in quantum information; quantum entanglement; quantum gravity

Citation Formats


                    DeWolfe, Oliver, Levin, Joshua, and Smith, Graeme. Multipartite optimized correlation measures and holography.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.102.066001.

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                    DeWolfe, Oliver, Levin, Joshua, & Smith, Graeme. Multipartite optimized correlation measures and holography.  United States.  https://doi.org/10.1103/PhysRevD.102.066001

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                    DeWolfe, Oliver, Levin, Joshua, and Smith, Graeme. Tue .  
"Multipartite optimized correlation measures and holography".  United States.  https://doi.org/10.1103/PhysRevD.102.066001.

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@article{osti_1658651,

  title        = {Multipartite optimized correlation measures and holography},

  author       = {DeWolfe, Oliver and Levin, Joshua and Smith, Graeme},

  abstractNote = {We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced Q correlation and R correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.},

  doi          = {10.1103/PhysRevD.102.066001},

  journal      = {Physical Review D},

  number       = 6,

  volume       = 102,

  place        = {United States},

  year         = {2020},

  month        = {9}

}

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Works referenced in this record:

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Title: Multipartite optimized correlation measures and holography

Abstract

Citation Formats

Multiboundary wormholes and holographic entanglement journal, September 2014

Bit threads and holographic entanglement of purification journal, August 2019

Bit threads and holographic entanglement of purification journal, August 2019

Holographic entanglement contour, bit threads, and the entanglement tsunami journal, July 2019

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

Holographic duality from random tensor networks journal, November 2016

Bit Threads and Holographic Entanglement journal, November 2016

Quantum and classical correlations inside the entanglement wedge journal, December 2019

The connection between holographic entanglement and complexity of purification journal, September 2019

Geometric aspects of holographic bit threads journal, May 2019

Entanglement of purification through holographic duality journal, March 2018

Generalizations of reflected entropy and the holographic dual journal, March 2020

A covariant holographic entanglement entropy proposal journal, July 2007

Information Theoretical Analysis of Multivariate Correlation journal, January 1960

Handlebody phases and the polyhedrality of the holographic entropy cone journal, October 2017

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

Entanglement wedge reconstruction and entanglement of purification journal, August 2018

Holographic Entropy Relations journal, September 2018

Towards entanglement of purification for conformal field theories journal, June 2018

Coarse graining holographic black holes journal, May 2019

Linear dependence structure of the entropy space journal, December 1975

Decoding the Apparent Horizon: Coarse-Grained Holographic Entropy journal, November 2018

Energy-constrained two-way assisted private and quantum capacities of quantum channels journal, June 2018

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories journal, May 2019

Bit Threads and Holographic Monogamy journal, July 2019

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

The Quantum Capacity With Symmetric Side Channels journal, September 2008

The entanglement of purification journal, September 2002

Entanglement wedge cross section from CFT: dynamics of local operator quench journal, February 2020

Optimized Measures of Bipartite Quantum Correlation journal, June 2020

Holographic entropy cone for five regions journal, July 2019

The Holographic Entropy Arrangement journal, February 2019

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

Towards a bit threads derivation of holographic entanglement of purification journal, July 2019

Superbalance of holographic entropy inequalities journal, July 2020

Computable measure of entanglement journal, February 2002

Squashed Entanglement for Multipartite States and Entanglement Measures Based on the Mixed Convex Roof journal, July 2009

Entanglement of purification and multiboundary wormhole geometries journal, February 2019

Holographic inequalities and entanglement of purification journal, March 2018

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

Conditional and multipartite entanglements of purification and holography journal, February 2019

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

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

Distributed compression and multiparty squashed entanglement journal, March 2008

Entanglement wedge cross sections require tripartite entanglement journal, April 2020

Optimized correlation measures in holography journal, March 2020

Correlation measures and distillable entanglement in AdS / CFT journal, February 2020

Quantum vs. classical information: operator negativity as a probe of scrambling journal, January 2020

Some aspects of entanglement wedge cross-section journal, May 2019

The inequalities of quantum information theory journal, April 2003

Derivation of Holographic Negativity in AdS 3 / CFT 2 journal, September 2019

Holographic mutual information is monogamous journal, February 2013

Reflected entropy and entanglement wedge cross section with the first order correction journal, December 2019

The holographic entropy cone journal, September 2015

Holographic entropy relations repackaged journal, October 2019

Multiboundary wormholes and holographic entanglement
journal, September 2014

Bit threads and holographic entanglement of purification
journal, August 2019

Bit threads and holographic entanglement of purification
journal, August 2019

Holographic entanglement contour, bit threads, and the entanglement tsunami
journal, July 2019

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

Holographic duality from random tensor networks
journal, November 2016

Bit Threads and Holographic Entanglement
journal, November 2016

Quantum and classical correlations inside the entanglement wedge
journal, December 2019

The connection between holographic entanglement and complexity of purification
journal, September 2019

Geometric aspects of holographic bit threads
journal, May 2019

Entanglement of purification through holographic duality
journal, March 2018

Generalizations of reflected entropy and the holographic dual
journal, March 2020

A covariant holographic entanglement entropy proposal
journal, July 2007

Information Theoretical Analysis of Multivariate Correlation
journal, January 1960

Handlebody phases and the polyhedrality of the holographic entropy cone
journal, October 2017

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

Entanglement wedge reconstruction and entanglement of purification
journal, August 2018

Holographic Entropy Relations
journal, September 2018

Towards entanglement of purification for conformal field theories
journal, June 2018

Coarse graining holographic black holes
journal, May 2019

Linear dependence structure of the entropy space
journal, December 1975

Decoding the Apparent Horizon: Coarse-Grained Holographic Entropy
journal, November 2018

Energy-constrained two-way assisted private and quantum capacities of quantum channels
journal, June 2018

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
journal, May 2019

Bit Threads and Holographic Monogamy
journal, July 2019

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

The Quantum Capacity With Symmetric Side Channels
journal, September 2008

The entanglement of purification
journal, September 2002

Entanglement wedge cross section from CFT: dynamics of local operator quench
journal, February 2020

Optimized Measures of Bipartite Quantum Correlation
journal, June 2020

Holographic entropy cone for five regions
journal, July 2019

The Holographic Entropy Arrangement
journal, February 2019

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

Towards a bit threads derivation of holographic entanglement of purification
journal, July 2019

Superbalance of holographic entropy inequalities
journal, July 2020

Computable measure of entanglement
journal, February 2002

Squashed Entanglement for Multipartite States and Entanglement Measures Based on the Mixed Convex Roof
journal, July 2009

Entanglement of purification and multiboundary wormhole geometries
journal, February 2019

Holographic inequalities and entanglement of purification
journal, March 2018

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

Conditional and multipartite entanglements of purification and holography
journal, February 2019

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

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

Distributed compression and multiparty squashed entanglement
journal, March 2008

Entanglement wedge cross sections require tripartite entanglement
journal, April 2020

Optimized correlation measures in holography
journal, March 2020

Correlation measures and distillable entanglement in $AdS / CFT$
journal, February 2020

Quantum vs. classical information: operator negativity as a probe of scrambling
journal, January 2020

Some aspects of entanglement wedge cross-section
journal, May 2019

The inequalities of quantum information theory
journal, April 2003

Derivation of Holographic Negativity in ${AdS}_{3} / {CFT}_{2}$
journal, September 2019

Holographic mutual information is monogamous
journal, February 2013

Reflected entropy and entanglement wedge cross section with the first order correction
journal, December 2019

The holographic entropy cone
journal, September 2015

Holographic entropy relations repackaged
journal, October 2019