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Dakic, Vedral, and Brukner arXiv:1004.0190 (2010) introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. This measure is significant in capturing quantum correlations from a geometric perspective. In this brief report, we evaluate the geometric measure of quantum discord for an arbitrary state and obtain an explicit and tight lower bound. Furthermore, we reveal an intrinsic feature of geometric measure of quantum discord by showing that it actually coincides with a simpler quantity based on von Neumann measurements.
Luo et al. (Mon,) studied this question.