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.