Hierarchy of multipartite nonlocality in the nonsignaling scenario
  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. 
Xiaoxu Wang, Chengjie Zhang, Qing Chen, Sixia Yu, Haidong Yuan, C.H.   Oh
quant-ph