Entanglement density and gravitational thermodynamics

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

doi:10.1103/physrevd.91.106009

Entanglement density and gravitational thermodynamics

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

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
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
Related Public URLs	http://arxiv.org/abs/1412.5472

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