Wigner-approach-enabled detection of multipartite nonlocality using all different bipartitions

Distinct from Bell's approach, Wigner derived a form of local realist (LR) inequality which is quantummechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such a generalized Wigner inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present paper, this limitation has been overcome by formulating a further generalization of Wigner's approach through the derivation of a set of LR inequalities with respect to all different bipartitions of a N-partite system. Quantum-mechanical violations of all individual LR inequalities belonging to such a set would rigorously certify multipartite nonlocality by also providing a finer characterization of the nature of multipartite nonlocality in the following sense. The quantum-mechanical violation of any given inequality of our complete set of LR inequalities would enable identification of the corresponding bipartition which exhibits nonlocality. This is in contrast to other multipartite LR inequalities such as the Svetlichny inequality or its generalization that cannot be used to detect whether there is any particular bipartition which is nonlocally correlated. The efficacy of the scheme developed in this paper is illustrated for the tripartite and quadripartite states.

Automated summary

In this paper, a further generalization of Wigner's approach is presented by deriving a set of LR inequalities for all different bipartitions of a multipartite system. The violations of these inequalities rigorously certify the multipartite nonlocality and identify the corresponding bipartitions exhibiting nonlocality.