Uhlmann A.
Density Operators as an Area for Differential Geometry
(30K, LaTeX)

ABSTRACT.  It is shown how to extend the Geometry of the projective space
of pure states, equipped with the Fubini Study metric, to the
space of density operators. This results in a variant of the
metric of Bures which reflects the maximally possible transition
probabilities in the vector rpresentations of general (mixed)
states. In particular the geodesics are considered, and it is
suggested, that with this metric the set of all density operators
becomes a cell of a manifold all geodesics of which closes with
length $\pi$.
Written version of a talk at the Symposium on Mathematical Physics,
Nicolous Copernicus University, Torun 1992.