  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.
