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Entanglement density and gravitational thermodynamics · Around

2014

Entanglement density and gravitational thermodynamics

Bhattacharya, Jyotirmoy, Hubeny, Veronika E., Rangamani, Mukund et al.

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In an attempt to find a quasi-local 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 sub-additivity constrains the entanglement density to be positive semi-definite.
Examining this density in the holographic context, we map its positivity to a statement of integrated null energy condition in the gravity dual.

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