Recently, the principle of non-violation of Information Causality [Nature 461, 1101[Nature 461, (2009], has been proposed as one of the foundational properties of nature. We explore the Hardy's non-locality theorem for two qubit systems, in the context of generalized probability theory, restricted by the principle of non-violation of Information Causality. Applying, a sufficient condition for Information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics, but still much less than what the no-signalling condition permits. We also study the Cabello type non-locality argument (a generalization of Hardy's argument) in this context.

Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy's nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy's argument.

We consider a hidden-variable theoretic description of successive measurements of non commuting spin observables on a input spin-s state. In this scenario, the hidden-variable theory leads to a Hardy-type argument that quantum predictions violate it. We show that the maximum probability of success of Hardy's argument in quantum theory is ( 1 2 ) 4s , which is more than in the spatial case.

Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett 106, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurementinduced nonlocality (MIN) for an arbitrary m×n dimensional bipartite density matrix ρ for the case where one of its reduced density matrix, ρ a , is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general, ρ a has d degenerate subspaces with dimension mi(mi ≤ m, i = 1, 2, ..., d). We show that according to the degeneracy of ρ a , if we expand ρ in a suitable basis, the evaluation of MIN for an m × n dimensional state ρ, is degraded to finding the MIN in the mi × n dimensional subspaces of state ρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary m × n state ρ for which mi ≤ 2, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. In the final, we explain the evaluation of MIN for 3 × n dimensional states in details.