Correlation measures and distillable entanglement in AdS/CFT

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 > 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.