  The minimal Bures distance of a quantum state of a bipartite system AB to the
set of classical states for subsystem A defines a geometric measure of quantum
discord. When A is a qubit, we show that this geometric quantum discord is
given in terms of the eigenvalues of a (2 n_B) x (2 n_B) hermitian matrix, n_B
being the Hilbert space dimension of the other subsystem B. As a first
application, we calculate the geometric discord for the output state of the
DQC1 algorithm. We find that it takes its highest value when the unitary matrix
from which the algorithm computes the trace has its eigenvalues uniformly
distributed on the unit circle modulo a symmetry with respect to the origin. As
a second application, we derive an explicit formula for the geometric discord
of two-qubit states with maximally mixed marginals and compare it with other
measures of quantum correlations. We also determine the closest classical
states to such two-qubit states.
