A new multi-partite entanglement measure and its holographic dual

TL;DR

This paper introduces a symmetric multi-party entanglement measure called multi-entropy, and proposes its holographic dual as a soap-film area, extending the understanding of entanglement in conformal field theories with gravity duals.

Contribution

It defines a new multi-partite entanglement measure and conjectures its holographic dual involving a soap-film area, generalizing previous entropy concepts.

Findings

Multi-entropy is symmetric and generalizes von Neumann entropy.

Holographic dual of multi-entropy is given by soap-film area.

Conjecture includes quantum corrections in the holographic prescription.

Abstract

In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate "soap-film" anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the sub-leading corrections in G_N.