Nonlocal correlations in the star-network configuration

The concept of bilocality was introduced to study the correlations which arise in an entanglement-swapping scenario, where one has two sources which can naturally be taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalization of the bilocality scenario; namely, the star network consisting of a single central party surrounded by $n$ edge parties, each of which shares an independent source with the center. We derive inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell-state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.

Figure 1

Star-network measurement scenario under the three-locality assumption.

Figure 2

The $n$-local set of probability distributions in the $(I,J)$ plane for the Bob $2\to 2$ scenario. The rotated square (with solid boundary) enclosing the $n$-local set is the boundary of the local set.