Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$

TL;DR

This paper investigates multipartite entanglement in holographic duals of BTZ black holes, revealing phase transitions and volume-law scaling in multi-entropy, with implications for understanding entanglement structure in AdS${}_3$/CFT${}_2$.

Contribution

It introduces a detailed analysis of multi-entropy and genuine multi-entropy in holographic black holes, uncovering new phase behavior and size dependence related to finite-cutoff holography.

Findings

Genuine tripartite multi-entropy exhibits volume-law scaling at high temperature.

A phase transition occurs when one subsystem exceeds half the total system, reducing entanglement.

Genuine multi-entropy shows nontrivial size dependence with radial cutoff.

Abstract

We study multipartite entanglement in typical pure states holographically dual to pure BTZ black holes, using multi-entropy and its ``genuine'' version. In the bulk, these quantities are computed by minimal geodesic networks (so-called Steiner trees). We find that at sufficiently high temperature, the genuine tripartite multi-entropy exhibits a volume-law scaling in sharp contrast to vacuum AdS$_3$, where the genuine contribution is universal and size-independent. Moreover, we find another phase: once one subsystem exceeds half of the total system, the leading genuine tripartite entanglement vanishes and reduces to that for global AdS${}_3$. This transition is indeed consistent with recent arguments for distillable EPR pairs in tripartite Haar-random states. Motivated by finite-cutoff holography, we further study the radial cutoff dependence of multi-entropy and show that genuine multi-entropy acquires nontrivial size dependence even for the tripartite case in AdS${}_3$. As a byproduct, we also observe an intriguing ``area-law'' contribution to multi-entropy that is relevant to vacuum AdS${}_3$.