Compact Bell inequalities for multipartite experiments

A method for construction of 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. An iterative method for deriving $(N+1)$-partite CHSH-type Bell inequalities from $N$-partite ones is derived. As an application, compact Bell inequalities for eight observers involving just four correlation functions are proposed. They require much less experimental effort than standard methods and thus are experimentally friendly in multiphoton experiments.