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arXiv · 1911.07852

Entanglement Wedge Cross Sections Require Tripartite Entanglement

Chris Akers·Pratik Rath
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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 $E_W$. If $E_W$ is related to either the CFT's reflected entropy or its entanglement of purification, then those quantities can differ from the mutual information at $\mathcal{O}(\frac{1}{G_N})$. We prove that this implies holographic CFT states must have $\mathcal{O}(\frac{1}{G_N})$ amounts of tripartite entanglement. This proof involves a new Fannes-type inequality for the reflected entropy, which itself has many interesting applications.

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Chris Akers, Pratik Rath. 2020-04-06. Entanglement Wedge Cross Sections Require Tripartite Entanglement. https://doi.org/10.1007/jhep04(2020)208

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