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.
@article{arxiv.1306.6860,
title = {Detecting non-locality in multipartite quantum systems with two-body correlation functions},
author = {J. Tura and R. Augusiak and A. B. Sainz and T. Vértesi and M. Lewenstein and A. Acín},
journal= {arXiv preprint arXiv:1306.6860},
year = {2014}
}