Entanglement Combing

We show that all multipartite pure states can, under local operations, be transformed into bipartite pairwise entangled states in a “lossless fashion”: An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol—decorrelating all other parties from each other—in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bipartite pairs is also classified. Finally, we point out several applications of this protocol as a useful primitive in quantum information theory.

Figure 1

Entanglement combing: An arbitrary multipartite entangled pure state $|\varphi {⟩}_{A,B_1,\cdots ,B_m}$ can be asymptotically deterministically transformed into a tensor product of bipartite states $|{\varphi }_1{⟩}_{A_1,B_1}\otimes \cdots \otimes |{\varphi }_m{⟩}_{A_m,B_m}$ under LOCC operations, in a way such that the bipartite entanglement between $A$ on the one hand and $B_1,\dots ,B_m$ on the other hand is preserved.