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:
-
- 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; 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. https://doi.org/10.1209/0295-5075/121/60007
Bao, Ning, and Remmen, Grant N. Fri .
"Bulk connectedness and boundary entanglement". United States. https://doi.org/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 = {Fri May 18 00:00:00 EDT 2018},
month = {Fri May 18 00:00:00 EDT 2018}
}
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Works referencing / citing this record:
Area Law Unification and the Holographic Event Horizon
text, January 2018
- Nomura, Yasunori; Remmen, Grant N.
- arXiv
Complexity change under conformal transformations in AdS3/CFT2
journal, May 2019
- Flory, Mario; Miekley, Nina
- Journal of High Energy Physics, Vol. 2019, Issue 5
Complexity change under conformal transformations in AdS$_{3}$/CFT$_{2}$
text, January 2018
- Flory, Mario; Miekley, Nina
- arXiv