  We explore a conformal field theoretic interpretation of the holographic
entanglement of purification, which is defined as the minimal area of
entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic
entanglement of purification agrees with the entanglement entropy for a
purified state, obtained from a special Weyl transformation, called
path-integral optimizations. By definition, this special purified state has the
minimal path-integral complexity. We confirm this claim in several examples.
