The categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality Articles uri icon

publication date

  • June 2023


  • 16-17


  • 38

International Standard Serial Number (ISSN)

  • 0217-7323

Electronic International Standard Serial Number (EISSN)

  • 1793-6632


  • An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theory of quantum information that embraces both classical and quantum information theories in a natural way, while also allowing to formalize the notion of quantum environment. A first application of these ideas is provided by extending the notion of statistical manifold to incorporate categories, and investigating a possible, uniparametric Cramer-Rao inequality in this setting.


  • categories; cramer-rao inequality; groupoids; markov morphisms; quantum information; states; statistical category; von neumann algebras