Recently Bell-type inequalities were introduced in Phys. Rev. A 85, 032119 (2012) to analyze the correlations emerging in an entanglement swapping scenario characterized by independence of the two sources shared between three parties. The corresponding scenario was referred to as bilocal scenario. Here, we derive Bell-type inequalities in n + 1 party scenario, i.e., in n-local scenario. Considering the two different cases with several number of inputs and outputs, we derive local and n-local bounds. The n-local inequality studied for two cases are proved to be tight. Replacing the sources by maximally entangled states for two binary inputs and two binary outputs and also for the fixed input and four outputs, we observe quantum violations of n-local bounds. But the resistance offered to noise cannot be increased as compared to the bilocal scenario. Thus increasing the number of parties in a linear fashion in source independent scenario does not contribute in lowering down the requirements of revealing quantumness in a network in contrast to the star configuration (Phys. Rev. A 90, 062109 (2014)) of n + 1 parties.

Standard tripartite nonlocality and genuine tripartite nonlocality can be detected by the violations of Mermin inequality and Svetlichny inequality, respectively. Since tripartite quantum nonlocality has novel applications in quantum information and quantum computation, it is important to investigate whether more than three observers can share tripartite nonlocality, simultaneously. In the present study we answer this question in the affirmative. In particular, we consider a scenario where three spin-1 2 particles are spatially separated and shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle; Bob performs measurements on the second particle and multiple Charlies perform measurements on the third particle sequentially. In this scenario we investigate how many Charlies can simultaneously demonstrate standard tripartite nonlocality and genuine tripartite nonlocality with single Alice and single Bob. The interesting result revealed by the present study is that at most six Charlies can simultaneously demonstrate standard tripartite nonlocality with single Alice and single Bob. On the other hand, at most two Charlies can simultaneously demonstrate genuine tripartite nonlocality with single Alice and single Bob. Hence, the present study shows that standard tripartite nonlocality can be simultaneously shared by larger number of Charlies compared to genuine tripartite nonlocality in the aforementioned scenario, which implies that standard tripartite nonlocality is more effective than genuine tripartite nonlocality in the context of simultaneous sharing by multiple observers.

According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the 99-th facet of N S2 local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A 88, 014102 (2013)), to reveal genuine tripartite nonlocality of generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended GHZ class states([1]) thereby proving the conjecture given by Bancal, et.al.[31] for the GGHZ class and the subclass of extended GHZ states. We compare the violation of this inequality with Svetlichny inequality which reveals the efficiency of the former inequality over the latter to demonstrate genuine nonlocality using the above classes of quantum states. Even in some cases discord monogamy score can be used as a better measure of quantum correlation over Svetlichny inequality for those classes of pure states. Besides, the 99-th facet inequality is found efficient not only for revealing genuine nonlocal behavior of correlations emerging in systems using pure entangled states but also in some cases of mixed entangled states over Svetlichny inequality and some well known measures of entanglement .

PACS 03.65.Ud -Entanglement and quantum nonlocality PACS 03.67.-a -Quantum Information Abstract -The relation between Bell-CHSH violation and factorization of Hilbert space is considered here. That is, a state which is local in the sense of the Bell-CHSH inequality under a certain factorization of the underlying Hilbert space can be Bell-CHSH non-local under a different factorization. While this question has been addressed with respect to separability , the relation of the factorization with Bell-CHSH violation has remained hitherto unexplored. We find here, that there is a set containing density matrices which do not exhibit Bell-CHSH violation under any factorization of the Hilbert space brought about by global unitary operations. Using the Cartan decomposition of SU (4),we characterize the set in terms of a necessary and sufficient criterion based on the spectrum of density matrices. Sufficient conditions are obtained to characterize such density matrices based on their bloch representations. For some classes of density matrices, necessary and sufficient conditions are derived in terms of bloch parameters. Furthermore, an estimation of the volume of such density matrices is achieved in terms of purity. The criterion is applied to some well-known class of states in two qubits.Since, both local filtering and global unitary operations influence Bell-CHSH violation of a state, a comparative study is made between the two operations. The inequivalence of the two operations(in terms of increasing Bell-CHSH violation) is exemplified through their action on some classes of states.

Violation of Bell inequality (or, Bell-type inequalities) by nonlocal correlations is justified by relaxation of at least one of the plausible physical constraints used to model such inequality. Based on this fact, in this letter we present a procedure to simulate three-qubit GHZ correlation relaxing two constraints, determinism and no signaling simultaneously. We have also derived the minimum amount of indeterminism and signaling to be introduced in a system. The corresponding number of signaling and local bits of mutual information needed to communicate are also provided and thus we are able to focus on utility of relaxation of these two constraints as useful resources.In any experiment on a model consisting of at least two subsystems, the statistics of the experimental results develop ceratin correlations. When the model is based on quantum theory then in some cases the correlations simulated cannot be obtained by any local theory. This type of correlations are referred as non-local correlations. Non-local correlations show deviations from correlations that are developed in a local model. One can manifest such correlations by the violation of Bell inequality [1]. This inequality with the modifications known as Belltype inequalities, are capable of distinguishing local and non-local correlations. Violation of Bell-type inequalities by predictions made in quantum theory implies that this theory is capable of simulating non-local correlations.Several attempts made recently to simulate non-local correlations. The study of non-local correlations can be broadly classified into four distinct categories. One category frames non-local correlations as a resource in information processing; e.g., random number generators [2], device independent quantum key distribution [3-5], etc. Second category of study focusses on the question: "why quantum theory is not more non-local" [6]. Third group of researchers are interested to measure nonlocality. They have quantified non-locality as the minimal number of classical bits that are needed to communicate from one party to another in order to simulate the required correlation [7-10]. For example, Toner and Bacon [11] gave a protocol where one bit of communication was sufficient to generate singlet correlations(considering Von-Neumann measurements). In [12], it was shown that for classical simulation of an n-party GHZ state, at least n log 2 n − 2n bits of communication is necessary. Using single N-qubit entangling pulse in a network (fully connected) of qubits interacting by anisotropic Heisenberg exchange, one can also simulate GHZ correlations [13]. In [14], quantum mechanical predictions for measurements of arbitrary products of Pauli operators on GHZ state were generated using a local hidden variable model in which number of classical bits that was required to be communicated, varied linearly with the number of qubits used. N. Gisin [15] introduces a protocol that reproduces three-partite GHZ correlations with bounded communications. To be more specific, it was shown that total...