Quantum and Classical Correlations Inside the Entanglement Wedge

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.