Two qubits of a W state violate Bell's inequality beyond Cirel'son's bound

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Abstract
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.

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