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 nonclopen 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 nogo theorem to general, arbitrary partitions of the boundary manifolds into nonclopen 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:

 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)
 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 Institute of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Gordon and Betty Moore Foundation
 OSTI Identifier:
 1597933
 Grant/Contract Number:
 SC0011632; 822481306744PHPXH; DGE1144469; 776
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Europhysics Letters
 Additional Journal Information:
 Journal Volume: 121; Journal Issue: 6; Journal ID: ISSN 02955075
 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:10.1209/02955075/121/60007.
Bao, Ning, & Remmen, Grant N. Bulk connectedness and boundary entanglement. United States. doi:https://doi.org/10.1209/02955075/121/60007
Bao, Ning, and Remmen, Grant N. Fri .
"Bulk connectedness and boundary entanglement". United States. doi:https://doi.org/10.1209/02955075/121/60007. 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 nonclopen 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 nogo theorem to general, arbitrary partitions of the boundary manifolds into nonclopen 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 = {10.1209/02955075/121/60007},
journal = {Europhysics Letters},
number = 6,
volume = 121,
place = {United States},
year = {2018},
month = {5}
}
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Works referencing / citing this record:
Complexity change under conformal transformations in AdS3/CFT2
journal, May 2019
 Flory, Mario; Miekley, Nina
 Journal of High Energy Physics, Vol. 2019, Issue 5