# Towards Entanglement of Purification for Conformal Field Theories

## TL;DR

This paper proposes a method to compute the entanglement of purification in 2D holographic CFTs using conformal blocks with twist operators, linking it to bulk entanglement wedge cross sections.

## Contribution

It introduces a new formula connecting entanglement of purification to conformal blocks, supported by tensor network interpretation and applications to AdS${}_3$ and BTZ blackhole geometries.

## Key findings

- The formula matches the entanglement wedge cross section in the bulk.
- Supports the conjecture linking entanglement of purification to entanglement wedge cross section.
- Provides a new computational approach for mixed state entanglement in holography.

## Abstract

We argue that the entanglement of purification for two dimensional holographic CFT can be obtained from conformal blocks with internal twist operators. First, we explain our formula from the view point of tensor network model of holography. Then, we apply it to bipartite mixed states dual to subregion of AdS${}_3$ and the static BTZ blackhole 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.