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: Bures–Helstrom metric tensor; Cramer–Rao bound; Differential Geometry of C∗-algebras; Fisher–Rao metric tensor; Helstrom bound; Symmetric Logarithmic Derivative; estimation theory; information geometry.