Holographic multipartite entanglement from the upper bound of $n$-partite information
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917834931568640 |
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| author | Ju, Xin-Xiang Pan, Wen-Bin Sun, Ya-Wen Zhao, Yang |
| author_facet | Ju, Xin-Xiang Pan, Wen-Bin Sun, Ya-Wen Zhao, Yang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_07790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holographic multipartite entanglement from the upper bound of $n$-partite information Ju, Xin-Xiang Pan, Wen-Bin Sun, Ya-Wen Zhao, Yang High Energy Physics - Theory 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. |
| title | Holographic multipartite entanglement from the upper bound of $n$-partite information |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.07790 |