More on the upper bound of holographic n-partite information

Abstract

We show that there exists a huge amount of multipartite entanglement in holography by studying the upper bound for holographic n-partite information I_n that n − 1 fixed boundary subregions participate. We develop methods to find the n-th region E that makes I_n reach the upper bound. Through the explicit evaluation, it is shown that I_n, an IR term without UV divergence, could diverge when the number of intervals or strips in region E approaches infinity. At this upper bound configuration, we could argue that I_n fully comes from the n-partite global quantum entanglement. Our results indicate: fewer-partite entanglement in holography emerges from more-partite entanglement; n − 1 distant local subregions are highly n-partite entangling. Moreover, the relationship between the convexity of a boundary subregion and the multipartite entanglement it participates, and the difference between multipartite entanglement structure in different dimensions are revealed as well.