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

Journal Article:
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https://doi.org/10.1103/PhysRevD.102.066001

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