Holographic Entanglement of Purification

TL;DR

This paper investigates the holographic entanglement of purification, proposing it as a geometric dual to a bipartite correlation measure in mixed states, supported by inequalities and tensor network interpretations.

Contribution

It introduces the holographic entanglement of purification as a geometric quantity and demonstrates its properties and inequalities, linking it to bipartite correlations in holography.

Findings

The minimal cross section of the entanglement wedge satisfies specific inequalities.

It is proposed as a holographic dual of the entanglement of purification.

The entanglement of purification obeys strong superadditivity in holographic CFTs.

Abstract

We study properties of the minimal cross section of entanglement wedge which connects two disconnected subsystems in holography. In particular we focus on various inequalities which are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument which supports this identification based on a tensor network interpretation of holography. This implies that the entanglement of purification satisfies the strong superadditivity for holographic conformal field theories.