Characterizing the Nonlocal Correlations Created via Entanglement Swapping

Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. This additional assumption leads to stronger tests of nonlocality. We show, in particular, that an entangled pair generated through entanglement swapping will already violate a Bell-type inequality for visibilities as low as 50% under our assumption.

Figure 1

Two-dimensional slice of the correlation space, which contains the points $P_Q$, $P_C$, ${\overline{P}}_C$, and $P_R$ defined in the text. The square delimits the quantum correlations achievable with entanglement swapping, which coincides with the local polytope in this slice. These correlations cannot be all reproduced locally with two independent sources. The four portions of parabola delimit the bilocal set [the upper parabola is obtained from (10). Similar quadratic Bell-type inequalities can be derived to obtain the other three parabolas]. The quantum point $P_Q$ enters the bilocal region for a visibility $v\le 1/2$.