More on the upper bound of holographic n-partite information

TL;DR

This paper investigates the upper bounds of holographic n-partite information, revealing extensive multipartite entanglement in holography and its dependence on boundary subregion configurations.

Contribution

It develops methods to identify the region maximizing n-partite information and analyzes the divergence and structure of multipartite entanglement in holographic systems.

Findings

n-partite information can diverge with infinite regions

multipartite entanglement emerges from fewer-partite entanglement

highly n-partite entangling of distant subregions

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.