Towards a bit threads derivation of holographic entanglement of purification
Abstract
We apply the bit thread formulation of holographic entanglement entropy to reduced states describing only the geometry contained within an entanglement wedge. We argue that a certain optimized bit thread configuration, which we construct, gives a purification of the reduced state to a full holographic state obeying a precise set of conditional mutual information relations. When this purification exists, we establish, under certain assumptions, the conjectured E_{P} = E_{W} relation equating the entanglement of purification with the area of the minimal cross section partitioning the bulk entanglement wedge. Along the way, we comment on minimal purifications of holographic states, geometric purifications, and black hole geometries.
 Authors:

 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 KU Leuven, Leuven (Belgium)
 Univ. of British Columbia, Vancouver, BC (Canada)
 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (SC21)
 OSTI Identifier:
 1566868
 Report Number(s):
 BNL2121272019JAAM
Journal ID: ISSN 10298479
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2019; Journal Issue: 7; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; AdSCFT Correspondencel; Black Holes; Gaugegravity correspondence
Citation Formats
Bao, Ning, ChatwinDavies, Aidan, Pollack, Jason, and Remmen, Grant N. Towards a bit threads derivation of holographic entanglement of purification. United States: N. p., 2019.
Web. doi:10.1007/JHEP07(2019)152.
Bao, Ning, ChatwinDavies, Aidan, Pollack, Jason, & Remmen, Grant N. Towards a bit threads derivation of holographic entanglement of purification. United States. doi:10.1007/JHEP07(2019)152.
Bao, Ning, ChatwinDavies, Aidan, Pollack, Jason, and Remmen, Grant N. Thu .
"Towards a bit threads derivation of holographic entanglement of purification". United States. doi:10.1007/JHEP07(2019)152. https://www.osti.gov/servlets/purl/1566868.
@article{osti_1566868,
title = {Towards a bit threads derivation of holographic entanglement of purification},
author = {Bao, Ning and ChatwinDavies, Aidan and Pollack, Jason and Remmen, Grant N.},
abstractNote = {We apply the bit thread formulation of holographic entanglement entropy to reduced states describing only the geometry contained within an entanglement wedge. We argue that a certain optimized bit thread configuration, which we construct, gives a purification of the reduced state to a full holographic state obeying a precise set of conditional mutual information relations. When this purification exists, we establish, under certain assumptions, the conjectured EP = EW relation equating the entanglement of purification with the area of the minimal cross section partitioning the bulk entanglement wedge. Along the way, we comment on minimal purifications of holographic states, geometric purifications, and black hole geometries.},
doi = {10.1007/JHEP07(2019)152},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 7,
volume = 2019,
place = {United States},
year = {2019},
month = {7}
}
Web of Science
Figures / Tables:
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