Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C ∗ -Algebras

Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C ∗ -Algebras

A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models wit...

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Veröffentlicht in:Entropy (Basel, Switzerland) Switzerland), 2020-11, Vol.22 (11), p.1332
Hauptverfasser: Ciaglia, Florio M, Jost, Jürgen, Schwachhöfer, Lorenz
Format: Artikel
Sprache:eng
Schlagworte:
Bures–Helstrom metric tensor
Cramer–Rao bound
estimation theory
Fisher–Rao metric tensor
Helstrom bound
information geometry
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Zusammenfassung:A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.
ISSN:1099-4300
1099-4300
DOI:10.3390/e22111332