CTC assisted PR box type correlation can lead to signaling

One of the most intriguing features of quantum physics is the nature of correlations present in the composite systems. This correlations can be captured by the amount of entanglement present in the system [1]. It is well known that the quantum mechanical correlations can violate Bell like inequalities, but are not strong enough to violate the causality. If we take the no signaling principle as an upper bound to all possible admissible correlations that nature allows, then it is interesting to find out if there exists any such correlations that go beyond quantum limit without violating causality [2, 3]. Popescu and Rohrlich constructed a hypothetical black box (PR box) which does exhibit correlations beyond the standard quantum limit in spite of being perfectly consistent with the no signaling criterion [2]. Recently, there have been lot of interest in investigating the power of the PR boxes. For example, it has been shown [4] that any two-output bipartite box can be simulated with the help of PR boxes. Furthermore, it turns out that there exists multiparty correlations which cannot be simulated by using n PR boxes for arbitrary n [4]. Some authors have also tried to find quantum mechanical realization of the PR box by focusing on the relations between causality and non locality in the context of preand post selected ensembles [5]. The authors in reference [6] have attempted to quantify the amount of non-locality contained in n noisy versions of the PR boxes. Two-party Gaussian states [7] have been used to probe experimentally non-local Popescu-Rohrlich correlations. The experiment is based on the spatial correlations of entangled photons and lens systems. A maximum violation of the CHSH inequality of 3.42 is obtained. This actually corresponds to the implementation of a non-local AND gate with success probability of 0.93. The PR boxes provide great power and resources to carry out information-theoretical tasks, but they cannot produce all types of multiparty correlations. It has also been seen that if one could clone a PR box, it could lead to signaling [8]. Quite analogous to a PR box, people have constructed other hypothetical boxes like M boxes to simulate the correlation of non maximally entangled states in two-qubit systems [9, 10]. These non local boxes were used to provide a winning strategy for the impossible coloring pseudo-telepathy game for the set of vectors having Kochen-Specker property in four dimension [11].