# Quantum and Classical Correlations Inside the Entanglement Wedge

## TL;DR

This paper explores the relationship between quantum and classical correlations within the entanglement wedge in holography, introducing a new geometrical measure called the entanglement wedge mutual information that captures more than just quantum entanglement.

## Contribution

It demonstrates that the entanglement wedge cross section can exceed quantum entanglement measures and introduces the entanglement wedge mutual information as a novel dual to the Q-correlation.

## Key findings

- EWCS can be larger than entanglement of formation.
- EWMI satisfies properties of Q-correlation and superadditivity.
- Both EWCS and EWMI capture classical correlations in holography.

## Abstract

We show that the entanglement wedge cross section (EWCS) can become larger than the quantum entanglement measures such as the entanglement of formation in the AdS/CFT correspondence. We then discuss a series of holographic duals to the optimized correlation measures, finding a novel geometrical measure of correlation, the \textit{entanglement wedge mutual information} (EWMI), as the dual of the $Q$-correlation. We prove that the EWMI satisfies the properties of the $Q$-correlation as well as the strong superadditivity, and that it can become larger than the entanglement measures. These results imply that both of the EWCS and the EWMI capture more than quantum entanglement in the entanglement wedge, which enlightens a potential role of classical correlations in holography.