# Holographic Entanglement of Purification from Conformal Field Theories

## TL;DR

This paper investigates the holographic entanglement of purification within conformal field theories, proposing a connection to minimal path-integral complexity states in AdS3/CFT2 and confirming this through multiple examples.

## Contribution

It introduces a conformal field theoretic interpretation of holographic entanglement of purification and links it to minimal complexity purified states in AdS3/CFT2.

## Key findings

- Holographic entanglement of purification matches entanglement entropy of a special purified state.
- The special purified state is obtained via a Weyl transformation called path-integral optimization.
- The approach is validated through several explicit examples.

## Abstract

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.