  From statistical distinguishability of probability distributions, one can
define distinguishability of quantum states. A corresponding measurement to
perform, optimal in a definite sense, for distinguishing between two given
states rho_A and rho_B, has been derived by Fuchs and Caves. We show that the
Bures-Uhlmann geodesic through the two states singles out this measurement. The
geodesic `bounces' at the boundary of the set of quantum states. Whenever the
geodesic hits the boundary, the state orthogonal to that boundary state is one
of the basis states for the measurement.
