Towards entanglement of purification for conformal field theories

Abstract

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 AdS3 and the static Ba'ados'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.