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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.
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