We find non-local but non-signaling probabilities satisfying the 'nonlocality without inequality’ arguments for multiple two-level systems. Maximum probability of success of these arguments are obtained in the framework of a generalized nonlocal theory. Interestingly, for two two-level systems, the probability of success of these arguments converge to a common maximum in this framework. This is in sharp contrast with the quantum case, where for such systems, Cabello’s argument succeeds more than that of Hardy’s. We also find that the maximum probability of success of Hardy’s argument is the same for both the two and three two-level systems in the framework of this more generalized theory.
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