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

Maximum quantum nonlocality between systems that never interacted