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Entanglement density and gravitational thermodynamics

Bhattacharya, J.; Hubeny, V.; Rangamani, M.; Takayanagi, T.

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Authors

J. Bhattacharya

V. Hubeny

M. Rangamani

T. Takayanagi



Abstract

In an attempt to find a quasilocal measure of quantum entanglement, we introduce the concept of entanglement density in relativistic quantum theories. This density is defined in terms of infinitesimal variations of the region whose entanglement we monitor and in certain cases can be mapped to the variations of the generating points of the associated domain of dependence. We argue that strong subadditivity constrains the entanglement density to be positive semidefinite. Examining this density in the holographic context, we map its positivity to a statement of integrated null energy condition in the gravity dual. We further speculate that this may be mapped to a statement analogous to the second law of black hole thermodynamics for the extremal surface.

Citation

Bhattacharya, J., Hubeny, V., Rangamani, M., & Takayanagi, T. (2015). Entanglement density and gravitational thermodynamics. Physical Review D, 91(10), Article 106009. https://doi.org/10.1103/physrevd.91.106009

Journal Article Type Article
Acceptance Date Jan 2, 2015
Online Publication Date May 21, 2015
Publication Date May 21, 2015
Deposit Date Dec 30, 2015
Publicly Available Date Jan 25, 2016
Journal Physical Review D - Particles, Fields, Gravitation, and Cosmology
Print ISSN 1550-7998
Electronic ISSN 1550-2368
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 91
Issue 10
Article Number 106009
DOI https://doi.org/10.1103/physrevd.91.106009
Public URL https://durham-repository.worktribe.com/output/1416089
Related Public URLs http://arxiv.org/abs/1412.5472

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Copyright Statement
Reprinted with permission from the American Physical Society: Physical Review D 91, 106009 © (2015) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.






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