Mixed State Entanglement Entropy in CFT

TL;DR

This paper introduces a subtraction method for calculating entanglement entropy in mixed states within conformal field theories, demonstrating its effectiveness in covariant bipartite systems and relating it to holographic duals.

Contribution

It presents a new subtraction approach for mixed state entanglement entropy calculation and establishes its equivalence with entanglement wedge cross sections in holographic duals.

Findings

The subtraction method effectively computes mixed state entanglement entropy.

The approach applies to covariant bipartite mixed states with explicit time dependence.

Entanglement entropy matches the entanglement wedge cross section in AdS/CFT examples.

Abstract

How to calculate the entanglement entropy between two subsystems for a mixed state has remained an important problem. In this paper, we provide a straightforward method, namely the subtraction approach, to solve this problem for generic covariant bipartite mixed states, where time dependence is explicitly included. We further demonstrate that the mixed state entanglement entropy $S_\text{vN}$ can be calculated in a more abstract yet powerful way. Within the context of the AdS$_3$/CFT$_2$ and a configuration of AdS$_5$/CFT$_4$ correspondences, we show that $S_\text{vN}$ exactly matches the corresponding entanglement wedge cross section in the AdS bulk, respectively.