Entanglement density and gravitational thermodynamics

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

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