On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
arXiv:2309.10428 · doi:10.1142/S0217732323500852
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.
20 pages, comments are welcome!
References in corpus (7)
- Uncertainty Principle and Quantum Fisher Information - II
- From the Jordan product to Riemannian geometries on classical and quantum states
- Schwinger's Picture of Quantum Mechanics IV: Composition and independence
- Quantum States, Groups and Monotone Metric Tensors
- Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
- A quantum route to the classical Lagrangian formalism
- Feynman's Propagator in Schwinger's picture of Quantum Mechanics