In Ads-CFT, the Ryu-Takayanagi Entanglement entropy formula gives a nice geometric interpretation (in the bulk) for the entanglement of a region in a CFT. Also, it is much easier to calculate the entanglement using the same instead of other methods like the replica trick.
But, Von-Neumann entropy is one in several measures of entanglement. So, is it possible that other entanglement measures might have similar geometric interpretation in the bulk? One can axiomatically right down the properties that a "good" entanglement measure should satisfy. If would be interesting to know what those constraints correspond to in the bulk.