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Title: Bulk connectedness and boundary entanglement

Abstract

Here we prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surface. We extend this no-go theorem to general, arbitrary partitions of the boundary manifolds into non-clopen parts, proving that the density matrix cannot be a tensor product. Finally, this result gives a necessary condition for states to potentially correspond to holographic duals.

Authors:
 [1];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics and Inst. for Quantum Information and Matter; Univ. of California, Berkeley, CA (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Gordon and Betty Moore Foundation
OSTI Identifier:
1597933
Grant/Contract Number:  
[SC0011632; 82248-13067-44-PHPXH; DGE-1144469; 776]
Resource Type:
Accepted Manuscript
Journal Name:
Europhysics Letters
Additional Journal Information:
[ Journal Volume: 121; Journal Issue: 6]; Journal ID: ISSN 0295-5075
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Bao, Ning, and Remmen, Grant N. Bulk connectedness and boundary entanglement. United States: N. p., 2018. Web. doi:10.1209/0295-5075/121/60007.
Bao, Ning, & Remmen, Grant N. Bulk connectedness and boundary entanglement. United States. doi:10.1209/0295-5075/121/60007.
Bao, Ning, and Remmen, Grant N. Fri . "Bulk connectedness and boundary entanglement". United States. doi:10.1209/0295-5075/121/60007. https://www.osti.gov/servlets/purl/1597933.
@article{osti_1597933,
title = {Bulk connectedness and boundary entanglement},
author = {Bao, Ning and Remmen, Grant N.},
abstractNote = {Here we prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surface. We extend this no-go theorem to general, arbitrary partitions of the boundary manifolds into non-clopen parts, proving that the density matrix cannot be a tensor product. Finally, this result gives a necessary condition for states to potentially correspond to holographic duals.},
doi = {10.1209/0295-5075/121/60007},
journal = {Europhysics Letters},
number = [6],
volume = [121],
place = {United States},
year = {2018},
month = {5}
}

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