Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation) allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in the x−y plane of the Bloch sphere on n-partite GHZ states. For the tripartite and fourpartite states, the models use only bipartite nonlocal boxes; they can be translated into classical communication schemes with finite average communication cost.