Peculiarities of quantum discord´s geometric measure

Some properties of the quantum discord based on the geometric measure advanced by Dakic et al (2010 Phys. Rev. Lett. 105 190502) are discussed here by recourse to a systematic survey of the two-qubit state-space, with emphasis on Werner and MEM states. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario. Some considerations regarding the XY model are also?made.