Towards entanglement of purification for conformal field theories

We argue that the entanglement of purification for 2D holographic conformal field theories (CFT) can be obtained from conformal blocks with internal twist operators. First, we explain our formula from the viewpoint of a tensor network model of holography. Then, we apply it to bipartite mixed states dual to a subregion of AdS(3) and the static Banados-Teitelboim-Zanelli black hole geometries. The formula in CFT agrees with the entanglement wedge cross section in the bulk, which has been recently conjectured to be equivalent to the entanglement of purification.