The most general class of nonlocality criteria for $N$-partite $d$-chotomic systems with $k$ number of measurement settings is derived under the constraint of measurement symmetries. It is the complete characterization of the multipartite nonlocality when the correlation is assumed to be symmetric under the choice of measurement settings. The generalized nonlocality condition is obtained using the correlation functions, which are derived from Fourier analysis of probability spectrums. It is found that the condition for the local hidden variable model is violated by multipartite quantum states and general constraints for the quantum violation of the maximally entangled state has been obtained.

• Received 23 May 2017

DOI:https://doi.org/10.1103/PhysRevA.98.022116