  The Riemannian Bures metric on the space of (normalized) complex positive
matrices is used for parameter estimation of mixed quantum states based on
repeated measurements just as the Fisher information in classical statistics.
It appears also in the concept of purifications of mixed states in quantum
physics. Here we determine its scalar curvature and Ricci tensor and prove a
lower bound for the curvature on the submanifold of trace one matrices. This
bound is achieved for the maximally mixed state, a further hint for the quantum
statistical meaning of the scalar curvature.
