Maximum quantum nonlocality between systems that never interacted

We show that there is a stronger form of bipartite quantum nonlocality in which systems that never interacted are as nonlocal as allowed by no-signaling. For this purpose, we first show that nonlocal boxes, theoretical objects that violate a bipartite Bell inequality as much as the no-signaling principle allows and which are physically impossible for most scenarios, are feasible if the two parties have 3 measurements with 4 outputs. Then we show that, in this case, entanglement swapping allows us to prepare mixtures of nonlocal boxes using systems that never interacted.

► We show quantum correlations as nonlocal as allowed by no-signaling between systems that never interacted.
► We show that nonlocal boxes are feasible if 2 parties have 3 measurements with 4 outputs.
► Experimental implementations of 1 and 2 are proposed.