Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C*-Algebras Articles uri icon

publication date

  • November 2020


  • 11:1332


  • 22

International Standard Serial Number (ISSN)

  • 1099-4300


  • 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.


  • information geometry; estimation theory; fisher–rao metric tensor; bures–helstrom metric tensor; cramer–rao bound; helstrom bound; symmetric logarithmic derivative; differential geometry of c∗-algebras