We propose a hierarchy of Bell-type inequalities for arbitrary n-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling m-locality, we show that the observed joint probabilities in any nonsignaling m-local realistic models should satisfy the (m−1)-th Bell-type inequality. When m=2 the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when m=n the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.
@article{arxiv.1608.03084,
title = {Hierarchy of multipartite nonlocality in the nonsignaling scenario},
author = {Xiaoxu Wang and Chengjie Zhang and Qing Chen and Sixia Yu and Haidong Yuan and C. H. Oh},
journal= {arXiv preprint arXiv:1608.03084},
year = {2016}
}