Bell's theorem teaches us that there are quantum correlations that can not be simulated by just shared randomness (Local Hidden variable). There are some recent results which simulate singlet correlation by using either 1 cbit or a binary (no-signaling) correlation which violate Bell's inequality maximally. But there is one more possible way to simulate quantum correlation by relaxing the condition of independency of measurement on shared randomness. Recently, MJW Hall showed that the statistics of singlet state can be generated by sacrificing measurement independence where underlying distribution of hidden variables depend on measurement direction of both parties [Phys. Rev. Lett.105 250404 (2010)].
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 analyze Hardy's non-locality argument for two spin-s systems and show that earlier solution in this regard was restricted due to imposition of some conditions which have no role in the argument of non-locality. We provide a compact form of non-locality condition for two spin-s systems and extend it to n number of spin-s particles. We also apply more general kind of non-locality argument still without inequality, to higher spin system.
Non existence of Universal Flipper for arbitrary quantum states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of qubits that can be flipped by a single machine is a great circle of the Bloch-sphere. In this paper, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of "non-increase of entanglement under LOCC". Interestingly, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle.
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