Spheres and hemispheres as quantum state spaces
Spheres and hemispheres allow an interpretation as quantum state spaces quite similar as to projective spaces. Spheres describe systems with two levels of equal degeneracy. The geometric key lies in the relation between transition probability and geodesics. There are isometric embeddings as geodesic submanifolds into the space of density operators, assuming the latter is equipped with the Bures metric. Then parallel transport is considered. Manageable expressions for parallel transport along geodesics arcs and polygons can be given.
scientific article; zbMATH DE number 1002998