The aim of this work is to lay down a formalism for parametric models that encapsulates both Classical and Quantum Information Geometry.
This will be done introducing parametric models on spaces of normal positive linear functionals on W*-algebras and providing a way of defining a Riemannian structure on this models that comes from the Jordan product of the W*-algebra. This Riemannian structure will have some features that are appealing from the
viewpoint of Information Geometry. After introducing this W*-algebraic framework, we will move to Estimation Theory. We will see how and to what extent it is possible to formulate in this framework two well-known statistical bounds: the Cramér-Rao bound and the Helstrom bound.
Finally, we will explicitly construct some examples that show how it is possible
to reduce this general framework to obtain well-known structures in Classical and Quantum Information Geometry.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:92108 |
| Date | 17 June 2024 |
| Creators | Di Nocera, Fabio |
| Contributors | Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English, German |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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