Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras

Florio Maria Ciaglia, Jürgen Jost, and Lorenz J. Schwachhöfer

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Submission date: 27. Oct. 2020
Pages: 34
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Abstract:
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.