Tripartite correlation signal from multipartite entanglement of purification

A bstract We propose a signal $$ {\Delta }_p^{(3)} $$ ∆ p 3 for tripartite correlations in finite-dimensional quantum systems and $$ {\Delta }_w^{(3)} $$ ∆ w 3 for holographic systems. We prove that $$ {\Delta }_p^{(3)} $$ ∆ p 3 is non-negative for any tripartite entangled mixed states and vanishes for mixed product states. It is a correlation signal because it is generally nonzero for a separable state containing a classical mixture. 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 correlation signal 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 correlation signals $$ {\Delta}_p^{(n)}\left({A}_1:\cdots :{A}_n\right) $$ Δ p n A 1 : ⋯ : A n .