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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, 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.

Authors:
ORCiD logo; ;
Publication Date:
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.
Levin, Joshua, DeWolfe, Oliver, & Smith, Graeme. Correlation measures and distillable entanglement in AdS / CFT. United States. doi:10.1103/PhysRevD.101.046015.
Levin, Joshua, DeWolfe, Oliver, and Smith, Graeme. Thu . "Correlation measures and distillable entanglement in AdS / CFT". United States. doi:10.1103/PhysRevD.101.046015.
@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 = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.101.046015

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Cited by: 5 works
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