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Recently, Gallego et al. [ Phys. Rev. Lett. 107 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and postquantum correlation must be intrinsically multipartite in nature. We establish similar results by using the device-independent success probability of Hardy's nonlocality argument for tripartite quantum systems. We construct an example of a tripartite Hardy correlation which is postquantum but satisfies not only the all-bipartite information principle but also the guess-your-neighbor's-input (GYNI) inequality.
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