Spheres and hemispheres as quantum state spaces
type: Item
instance of: scholarly article
title: Spheres and hemispheres as quantum state spaces
zbMATH Open document ID: 0878.53053
DOI: 10.1016/0393-0440(95)00004-6
author: Armin Uhlmann
published in: Journal of Geometry and Physics
publication date: 1997-04-23T00:00:00Z
review text: 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.
reviewed by: L.Lanz and A.Loinger
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 81S99
zbMATH DE Number: 1002998
zbMATH Keywords: spheres
zbMATH Keywords: hemispheres
zbMATH Keywords: quantum state spaces
zbMATH Keywords: geodesic submanifolds
zbMATH Keywords: space of density operators
zbMATH Keywords: parallel transport
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00004-6
OpenAlex ID: W2132384201
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description: scientific article; zbMATH DE number 1002998