Armin Uhlmann
Spheres and Hemispheres as Quantum State Spaces
The paper is published: J. Geom. Phys. 18, 1 (1996) 76-92

MSC:

58B99 None of the above but in this section

81Q99 None of the above but in this section

Abstract: Spheres and hemispheres allow for their interpretation as quantum
states spaces quite similar as it is known about projective spaces.
Spheres describe systems with two levels of equal degeneracy.
The geometric key is in the relation between transition probability
and geodesics. \hfill \\
There are isometric embeddings as geodesic
submanifolds into the space of density operators assuming the latter is
equipped with the Bures metric. Then parallel transporting is
considered. Managable expressions for the
parallel transport along geodesic arcs and polygons can be given.

Keywords: quantum state spaces