Genuine multi-entropy and holography
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908426158735360 |
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| author | Iizuka, Norihiro Nishida, Mitsuhiro |
| author_facet | Iizuka, Norihiro Nishida, Mitsuhiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Genuine multi-entropy and holography Iizuka, Norihiro Nishida, Mitsuhiro High Energy Physics - Theory Quantum Physics 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. |
| title | Genuine multi-entropy and holography |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2502.07995 |