Related papers: On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality

On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality

URL: http://arxiv.org/abs/2309.10428v1
Date: Tue, 19 Sep 2023 08:45:13 GMT
Title: On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
Authors: Florio M. Ciaglia, Fabio Di Cosmo, Laura Gonz\'alez-Bravo, Alberto Ibort, Giuseppe Marmo
Abstract summary: 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 theory in a natural way.
Score: 0.0
License: http://creativecommons.org/licenses/by-sa/4.0/
Abstract: 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 theory in a natural way, while also allowing to formalise 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.

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