Entanglement of Purification in Random Tensor Networks

Chris Akers; Thomas Faulkner; Simon Lin; Pratik Rath

paper

Entanglement of Purification in Random Tensor Networks

arXiv:2306.06163

Abstract

The entanglement of purification $E_{P} (A : B)$ is a powerful correlation measure, but it is notoriously difficult to compute because it involves an optimization over all possible purifications. In this paper, we prove a new inequality: $E_{P} (A : B) \geq \frac{1}{2} S_{R}^{(2)} (A : B)$ , where $S_{R}^{(n)} (A : B)$ is the Renyi reflected entropy. Using this, we compute $E_{P} (A : B)$ for a large class of random tensor networks at large bond dimension and show that it is equal to the entanglement wedge cross section $E W (A : B)$ , proving a previous conjecture motivated from AdS/CFT.

5 pages, double-sided, 5 figures