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Title: 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 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.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. KU Leuven, Leuven (Belgium)
  3. Univ. of British Columbia, Vancouver, BC (Canada)
  4. 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 (SC-21)
OSTI Identifier:
1566868
Report Number(s):
BNL-212127-2019-JAAM
Journal ID: ISSN 1029-8479
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; AdS-CFT Correspondencel; Black Holes; Gauge-gravity correspondence

Citation Formats

Bao, Ning, Chatwin-Davies, 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, Chatwin-Davies, 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, Chatwin-Davies, 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 Chatwin-Davies, 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)},
number = 7,
volume = 2019,
place = {United States},
year = {2019},
month = {7}
}

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Cited by: 4 works
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