Geodesics and the best measurement for distinguishing quantum states
  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. 
Asa Ericsson