Entanglement and Nonlocality are Inequivalent for Any Number of Parties

Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of parties.

Figure 1

Schematic depiction of our construction. The initial state ${\rho }_{AB}$ is entangled and local for generalized measurements. The application of properly chosen local channels ${\mathrm{\Lambda }}_{A\to S}$ and ${\mathrm{\Lambda }}_{B\to \overline{S}}$, with $S=A_1\dots A_L$ and $\overline{S}=A_{L+1}\dots A_N$, to ${\rho }_{AB}$ creates an $N$-partite state ${\sigma }_{\mathsf{A}}$ that is genuinely multipartite entangled and bilocal with respect to the bipartition $S|\overline{S}$. The dashed green line determines the locality cut.