Strong violations of Bell-type inequalities for Werner-like states

We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation of the Bell-Wigner and Janssens inequalities is obtained for a large range of the parameter $p$. The range given by these inequalities is greater than the one given by the Clauser-Horne inequality. The range in which a violation is attained actually coincides with the range where the Werner-like states are known to be nonseparable, i.e., for $p>1∕3$. However, the improvement over the Clauser-Horne inequality is achieved at the price of restricting the class of possible local hidden variable theories.