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arXiv · 2509.08209

Tripartite Correlation Signal from Multipartite Entanglement of Purification

Ning Bao·Keiichiro Furuya·Joydeep Naskar
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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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Ning Bao, Keiichiro Furuya, Joydeep Naskar. 2025-09-10. Tripartite Correlation Signal from Multipartite Entanglement of Purification. https://doi.org/10.1007/jhep05(2026)236

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