Mixed State Entanglement Entropy in CFT

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.

Published version in JHEP. Added clarifications and corrections. 19 pages, 9 figures