Genuine multi-entropy and holography

TL;DR

This paper introduces a new multi-entropy measure to analyze multipartite entanglement in holography, revealing that genuine multi-partite entanglement is significant and not negligible in holographic systems.

Contribution

It defines a genuine q-partite multi-entropy and demonstrates its importance in holography and black hole physics, especially after the Page time.

Findings

Non-bipartite multi-entropies are always positive in holography.

Genuine multi-partite entanglement is significant and not small.

The measure is crucial for understanding entanglement in black holes after the Page time.

Abstract

Is bipartite entanglement sufficient for holography? Through the analysis of the Markov gap, it is known that the answer is no. In this paper, we give a new perspective on this issue from a different angle using a multi-entropy. We define a genuine $\mathtt{q}$-partite multi-entropy from a $\mathtt{q}$-partite multi-entropy by subtracting appropriate linear combinations of $\mathtt{\tilde{q}}$-partite multi-entropies for $\mathtt{\tilde{q}} < \mathtt{q}$, in such a way that the genuine $\mathtt{q}$-partite multi-entropy vanishes for all $\mathtt{\tilde{q}}$-partite entangled states. After studying several aspects, we apply it to black holes and holography. For the application to black holes, we see that such a genuine $\mathtt{q}$-partite multi-entropy is important only after the Page time. For the application to holography, we prove that non-bipartite multi-entropies are always positive and $\mathcal{O}\left({1/ G_N}\right)$, as long as boundary subregions are connected. This indicates that for holography, genuine multi-partite entanglement is not small and plays an important role.