We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of the 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 minimal path-integral complexity. We confirm this claim in several examples.
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Caputa et al. (2019) studied this question.
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