Genuine multi-entropy and holography

• URL: http://arxiv.org/abs/2502.07995v5
• Date: Sun, 29 Jun 2025 13:39:58 GMT
• Title: Genuine multi-entropy and holography
• Authors: Norihiro Iizuka, Mitsuhiro Nishida,
• Abstract summary: We show that for holography, genuine multi-partite entanglement is not small and plays an important role.<n>For the application to black holes, we see that such a genuine $mathttq$-partite multi-entropy is important only after the Page time.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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