Detecting non-locality in multipartite quantum systems with two-body correlation functions

Bell inequalities define experimentally observable quantities to detect non-locality. In general, they involve correlation functions of all the parties. Unfortunately, these measurements are hard to implement for systems consisting of many constituents, where only few-body correlation functions are accessible. Here we demonstrate that higher-order correlation functions are not necessary to certify nonlocality in multipartite quantum states by constructing Bell inequalities from one- and two-body correlation functions for an arbitrary number of parties. The obtained inequalities are violated by some of the Dicke states, which arise naturally in many-body physics as the ground states of the two-body Lipkin-Meshkov-Glick Hamiltonian.