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

Abstract

A geometrical formulation of estimation theory for finite-dimensional $C^{\star }$-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.

33 pages. Minor improvements. References added. Comments are welcome!

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• G-dual teleparallel connections in Information Geometry
• On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
• A coadjoint orbit-like construction for Jordan superalgebras