2000 character limit reached
On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality (2309.10428v1)
Published 19 Sep 2023 in quant-ph, cs.IT, math-ph, math.IT, and math.MP
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.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
