Entanglement wedge cross sections require tripartite entanglement

A bstract 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 O(1/GN). O 1 G N . We prove that this implies holographic CFT states must have O(1/GN). O 1 G N . amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.