It is shown that the correlations between two qubits selected from a trio prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more than the correlations between two qubits in any quantum state. Such a violation beyond Cirel'son's bound is smaller than the one achieved by two qubits selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local observers can know from their own measurements whether their qubits belongs or not to the selected pair.
@article{arxiv.quant-ph/0205183,
title = {Two qubits of a W state violate Bell's inequality beyond Cirel'son's bound},
author = {Adan Cabello},
journal= {arXiv preprint arXiv:quant-ph/0205183},
year = {2009}
}