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Bulk Connectedness and Boundary Entanglement

Bao, Ning and Remmen, Grant N. (2018) Bulk Connectedness and Boundary Entanglement. Europhysics Letters, 121 (6). Art. No. 60007. ISSN 0295-5075. http://resolver.caltech.edu/CaltechAUTHORS:20170314-133758800

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Abstract

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. This result gives a necessary condition for states to potentially correspond to holographic duals.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1209/0295-5075/121/60007DOIArticle
http://arxiv.org/abs/1703.00018arXivDiscussion Paper
ORCID:
AuthorORCID
Bao, Ning0000-0002-3296-1039
Remmen, Grant N.0000-0001-6569-8866
Additional Information:© 2018 EPLA. Received 19 January 2018; Accepted 2 May 2018; Published 18 May 2018. We thank the referees for their helpful suggestions. We also thank Raphael Bousso, Sean Carroll, Netta Engelhardt, and Mukund Rangamani for useful discussions and comments. This research was supported in part by DOE grant DE-SC0011632 and by the Gordon and Betty Moore Foundation through Grant 776 to the Caltech Moore Center for Theoretical Cosmology and Physics. NB was supported at Caltech by the DuBridge postdoctoral fellowship at the Walter Burke Institute for Theoretical Physics and is currently supported at the University of California, Berkeley by the National Science Foundation under grant number 82248-13067-44-PHPXH. GNR was supported at Caltech by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship under Grant No. DGE-1144469 and is currently supported at University of California, Berkeley by the Miller Institute for Basic Research in Science.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter, IQIM, Moore Center for Theoretical Cosmology and Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Gordon and Betty Moore Foundation776
Lee A. DuBridge FellowshipUNSPECIFIED
NSF82248-13067-44-PHPXH
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
Miller Institute for Basic Research in ScienceUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2017-011
Classification Code:PACS: 04.60.-m; 04.20.-q; 03.65.-w
Record Number:CaltechAUTHORS:20170314-133758800
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170314-133758800
Official Citation:Ning Bao and Grant N. Remmen 2018 EPL 121 60007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75104
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:15 Mar 2017 18:34
Last Modified:06 Jun 2018 22:04

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