Tripartite Entanglement Signal from Multipartite Entanglement of Purification

• URL: http://arxiv.org/abs/2509.08209v1
• Date: Wed, 10 Sep 2025 00:43:36 GMT
• Title: Tripartite Entanglement Signal from Multipartite Entanglement of Purification
• Authors: Ning Bao, Keiichiro Furuya, Joydeep Naskar,
• Abstract summary: We prove that $Delta(3)_p$ is non-negative for any tripartite entangled mixed states.<n>We apply the tripartite entanglement measure to study the structures of tripartite entanglement in AdS$_3$/CFT$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a signal $\Delta^{(3)}_p$ for genuine tripartite entanglement in finite-dimensional quantum systems and $\Delta^{(3)}_w$ for holographic systems. We prove that $\Delta^{(3)}_p$ is non-negative for any tripartite entangled mixed states. Based on the conjecture, the equality between an entanglement wedge cross section $E_w$ and entanglement of purification $E_p$, i.e., $E_w = E_P$ in the semiclassical limit, we apply the tripartite entanglement measure to study the structures of tripartite entanglement in AdS$_3$/CFT$_2$, especially for pure AdS$_3$. We comment on a generalization to $n$-partite entanglement signals $\Delta^{(n)}_p(A_1:\cdots:A_n)$.

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