The Erwin Schrr Odinger International Institute for Mathematical Physics Spheres and Hemispheres as Quantum State Spaces Spheres and Hemispheres as Quantum State Spaces
نویسنده
چکیده
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. 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.
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