  We define a new measure of quantum correlations in bipartite quantum systems
given by the Bures distance of the system state to the set of classical states
with respect to one subsystem, that is, to the states with zero quantum
discord. Our measure is a geometrical version of the quantum discord. As the
latter it quantifies the degree of non-classicality in the system. For pure
states it is identical to the geometric measure of entanglement. We show that
for mixed states it coincides with the optimal success probability of an
ambiguous quantum state discrimination task. Moreover, the closest zero-discord
states to a given state are obtained in terms of the corresponding optimal
measurements.
