Abstract
We propose a signal Δ⁽³⁾_p for genuine tripartite entanglement in finite-dimensional quantum systems and Δ⁽³⁾_w for holographic systems. We prove that Δ⁽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 AdS₃/CFT₂, especially for pure AdS₃. We comment on a generalization to n-partite entanglement signals Δ⁽ⁿ⁾_p(A₁:…:A_n).