Holographic multipartite entanglement from the upper bound of $n$-partite information

TL;DR

This paper investigates the upper bounds of holographic n-partite information, revealing fundamental differences across dimensions and proposing that multipartite entanglement can be fully characterized at these bounds.

Contribution

It introduces the concept of the entanglement of state-constrained purification and analyzes the upper bounds of n-partite information in holographic CFTs across different dimensions.

Findings

Upper bounds of $-I_3$ relate to entanglement of state-constrained purification.

Finite upper bounds for $I_n$ in 1+1 dimensions; divergences in higher dimensions.

At upper bounds, $I_n$ fully captures multipartite entanglement.

Abstract

To analyze the holographic multipartite entanglement structure, we study the upper bound for holographic $n$-partite information $(-1)^n I_n$ that $n-1$ fixed boundary subregions participate together with an arbitrary region $E$. In general cases, we could find regions $E$ that make $I_n$ approach the upper bound. For $n=3$, we show that the upper bound of $-I_3$ is given by a quantity that we name the entanglement of state-constrained purification $EoSP(A:B)$. For $n\geq4$, we find that the upper bound of $I_n$ is finite in holographic CFT$_{1+1}$ but has UV divergences in higher dimensions, which reveals a fundamental difference in the entanglement structure in different dimensions. When $(-1)^n I_n$ reaches the information-theoretical upper bound, we argue that ( I_n ) fully accounts for multipartite global entanglement in these upper bound critical points, in contrast to usual cases where $I_n$ is not a perfect measure for multipartite entanglement. We further show that these results suggest that fewer-partite entanglement fully emerges from more-partite entanglement, and any $n-1$ distant regions are fully $n$-partite entangling in higher dimensions.