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Entanglement wedge cross sections require tripartite entanglement
Chris Akers (Massachusetts Institute of Technology), Pratik Rath (Lawrence Berkeley National Laboratory, University of California, Berkeley)
Abstract: 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 $$ O\left(\frac{1}{G_N}\right). $$ O 1 G N . We prove that this implies holographic CFT states must have $$ O\left(\frac{1}{G_N}\right). $$ 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.