Correlation measures and distillable entanglement in AdS/CFT

TL;DR

This paper investigates geometric interpretations of correlation measures in holography, revealing their connections to entanglement wedge cross-sections and mutual information, and establishing trade-offs with distillable entanglement.

Contribution

It introduces geometric interpretations of $Q$- and $R$-correlations in AdS/CFT, linking them to entanglement wedge cross-sections and mutual information.

Findings

$E_Q$ corresponds to minimal mutual information in the entanglement wedge.

$E_R$ coincides with the entanglement wedge cross-section.

A trade-off exists between minimal mutual information and distillable entanglement.

Abstract

Recent developments have exposed close connections between quantum information and holography. In this paper, we explore the geometrical interpretations of the recently introduced $Q$-correlation and $R$-correlation, $E_Q$ and $E_R$. We find that $E_Q$ admits a natural geometric interpretation via the surface-state correspondence: it is a minimal mutual information between a surface region $A$ and a cross-section of $A$'s entanglement wedge with $B$. We note a strict trade-off between this minimal mutual information and the symmetric side-channel assisted distillable entanglement from the environment $E$ to $A$, $I^{ss}(E\rangle A)$. We also show that the $R$-correlation, $E_R$, coincides holographically with the entanglement wedge cross-section. This further elucidates the intricate relationship between entanglement, correlations, and geometry in holographic field theories.