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⋆-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.