Entanglement Wedge Cross Section from the Dual Density Matrix

TL;DR

This paper introduces the odd entanglement entropy (OEE), a new information measure that allows computation of the entanglement wedge cross section in holographic conformal field theories, linking quantum information and geometry.

Contribution

The paper defines OEE and demonstrates its use in calculating the entanglement wedge cross section in 2D holographic CFTs, proposing a generalization to higher dimensions.

Findings

OEE computed explicitly for AdS3 and BTZ black hole

OEE matches the entanglement wedge cross section in these cases

Conjecture of the relation holding in all dimensions

Abstract

We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic CFTs. The entanglement wedge cross section has been introduced as a minimal cross section of the entanglement wedge, a natural generalization of the Ryu-Takayanagi surface. By using the replica trick, we explicitly compute the OEE for two-dimensional holographic CFT (AdS${}_3$ and planar BTZ blackhole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.