Violating Bell's inequality beyond Cirel'son's bound

Cirel'son inequality states that the absolute value of the combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH) inequality is bound by $2 \sqrt 2$. It is shown that the correlations of two qubits belonging to a three-qubit system can violate the CHSH inequality beyond $2 \sqrt 2$. Such a violation is not in conflict with Cirel'son's inequality because it requires a choice of pairs of qubits which is only meaningful in a local-realistic theory. The maximum allowed violation of the CHSH inequality, 4, can be achieved using the Greenberger-Horne-Zeilinger state.