More efficient Bell inequalities for Werner states

Abstract

In this paper we study the nonlocal properties of two-qubit Werner states parametrized by the visibility parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. A family of Bell inequalities is constructed that proves the two-qubit Werner states to be nonlocal for the parameter range $0.7056<p\ensuremath{\leqslant}1$. This is slightly wider than the range $0.7071<p\ensuremath{\leqslant}1$, corresponding to the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by Gisin in the positive, i.e., there exist Bell inequalities which are more efficient than the CHSH inequality in the sense that they are violated by a wider range of two-qubit Werner states.