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Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three and four-partite Bell inequalities constructed from one and two-body expectation values that obey translational symmetry, and show that they reveal nonlocality in multipartite states. Also, by providing a particular example of a five-partite Bell inequality, we show that nonlocality can be detected from two-body correlators involving only nearest neighbours. Finally, we demonstrate that any translationally invariant Bell inequality can be maximally violated by a translationally invariant state and the same set of observables at all sites. We provide a numerical algorithm allowing one to seek for maximal violation of a translationally invariant Bell inequality.
A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A unified frame
Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property for multi
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each make one of
D{u}r [Phys. Rev. Lett. {bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $Nge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating t
We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Be