Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional <i>C</i>^∗-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.

Keywords

• information geometry
• estimation theory
• Fisher–Rao metric tensor
• Bures–Helstrom metric tensor
• Cramer–Rao bound
• Helstrom bound