Entropy inequalities and Bell inequalities for two-qubit systems

The sufficient conditions for the nonviolation of the Bell-Clauser-Horne- Shimony-Holt inequalities in a mixed state of a two-qubit system were discussed. The conditions included, the linear entropy of the state is not smaller than 0.457, the sum of the conditional linear entropies is not smaller than -0.086 and von Neumann entropy is not smaller than 0.833. It was shown that separability implies the fulfilment of both Bell inequalities and quantum entropy inequalities. The results show that the Clauser-Horne-Shimony-Holt (CHSH) inequalities are necessary conditions for the existence of local hidden variables (LHV) theories.