Entanglement of purification in random tensor networks

The entanglement of purification EP(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: EP(A∶B)≥12SR(2)(A∶B), where SR(n)(A∶B) is the Renyi reflected entropy. Using this, we compute EP(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 EW(A∶B), proving a previous conjecture motivated from AdS/CFT.