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.
Highlights
Quantum entanglement has provided a key tool to study various aspects of modern physics from condensed matter theory to the black hole evaporation
We show that the conditional entanglement of mutual information (CEMI) reduces to half of the holographic mutual information as the R-correlation does to the entanglement wedge cross section (EWCS), when they are optimized over the geometrical extensions
Since there seems to be no reason to believe that these states are singular among the holographic states, we argue that the EWCS is generically larger than these entanglement measures in holographic CFTs
Summary
Quantum entanglement has provided a key tool to study various aspects of modern physics from condensed matter theory to the black hole evaporation. We show that the EWCS can be strictly larger than various entanglement measures at the leading order OðN2Þ It is shown in a holographic configuration near to the saturation of the ArakiLieb inequality [49,50]. We find that the holographic dual of the Qcorrelation provides us with a new bulk measure of correlation inside the entanglement wedge, which we call the entanglement wedge mutual information (EWMI). This quantity appropriately satisfies all of the properties of the Q-correlation, as well as the strong superadditivity like the EWCS. In the Appendix, we prove new inequalities of the multipartite EOP and the multipartite EWCS, complementing the work of [22]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
