Entanglement wedge cross sections require tripartite entanglement

Abstract

Abstract

We argue that holographic CFT states require a large amount of tripartite entanglement, in contrast to the conjecture that their entanglement is mostly bipartite. Our evidence is that this mostly-bipartite conjecture is in sharp conflict with two well- supported conjectures about the entanglement wedge cross section surface EW. If EW is related to either the CFT’s reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at O1GN.$$ O\left(\frac{1}{G_N}\right). $$ We prove that this implies holographic CFT states must have O1GN.$$ O\left(\frac{1}{G_N}\right). $$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.