Bell inequalities versus entanglement and mixedness for a class of two -   qubit states
  For a class of mixed two -qubit states we show that it is not possible to discriminate between states violating or non - violating Bell - CHSH inequalities, knowing only their entanglement and mixedness. For a large set of possible values of these quantities, we construct pairs of states with the same entanglement and mixedness such that one state is violating but the other is non - violating Bell - CHSH inequality. 
L. Derkacz and L. Jakobczyk