Correlation measures and distillable entanglement in AdS / CFT

Levin, Joshua; DeWolfe, Oliver; Smith, Graeme

doi:10.1103/PhysRevD.101.046015

Title: Correlation measures and distillable entanglement in $AdS / CFT$

Abstract

Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced Q-correlation and R-correlation, E_Q and E_R. We find that E_Q admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region A and a cross section of A’s entanglement wedge with B. We note a strict trade-off between this minimal mutual information and the symmetric side-channel-assisted distillable entanglement from the environment E to A, I^ss(E>A). We also show that the R-correlation, E_R, coincides holographically with the entanglement wedge cross section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories.

Authors:

; DeWolfe, Oliver; Smith, Graeme

Publication Date:: Thu Feb 13 00:00:00 EST 2020

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

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

OSTI Identifier:: 1599510

Alternate Identifier(s):: OSTI ID: 1762007

Grant/Contract Number:: SC0010005; SC0020386

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; 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; Gauge-gravity dualities; Quantum correlations in quantum information; Quantum gravity

Citation Formats


                    Levin, Joshua, DeWolfe, Oliver, and Smith, Graeme. Correlation measures and distillable entanglement in AdS / CFT.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.046015.

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                    Levin, Joshua, DeWolfe, Oliver, & Smith, Graeme. Correlation measures and distillable entanglement in AdS / CFT.  United States.  https://doi.org/10.1103/PhysRevD.101.046015

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                    Levin, Joshua, DeWolfe, Oliver, and Smith, Graeme. Thu .  
"Correlation measures and distillable entanglement in AdS / CFT".  United States.  https://doi.org/10.1103/PhysRevD.101.046015.

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@article{osti_1599510,

  title        = {Correlation measures and distillable entanglement in AdS / CFT},

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

  abstractNote = {Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced Q-correlation and R-correlation, EQ and ER. We find that EQ admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region A and a cross section of A’s entanglement wedge with B. We note a strict trade-off between this minimal mutual information and the symmetric side-channel-assisted distillable entanglement from the environment E to A, Iss(E>A). We also show that the R-correlation, ER, coincides holographically with the entanglement wedge cross section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories.},

  doi          = {10.1103/PhysRevD.101.046015},

  journal      = {Physical Review D},

  number       = 4,

  volume       = 101,

  place        = {United States},

  year         = {Thu Feb 13 00:00:00 EST 2020},

  month        = {Thu Feb 13 00:00:00 EST 2020}

}

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Works referenced in this record:

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Title: Correlation measures and distillable entanglement in AdS / CFT

Abstract

Citation Formats

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Title: Correlation measures and distillable entanglement in $AdS / CFT$

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