Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A categorical approach to the foundations of Quantum theory

Kevin Dunne

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.48730/p601-1q86

Related papers

Categorical Quantum Theory

Peter Nonnenmann

Springer eBooks•Jan 1, 2021•0 citations

Enrichment in Categorical Quantum Foundations

Mathys Rennela

•Jan 1, 2018•0 citations

Categorical Probabilistic Theories

Stefano Gogioso, Carlo Maria Scandolo

We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM and OPTs have found successful application to a number of areas in quantum foundations and information theory: they present many similarities, both in spirit and in formalism, but they remain separated by a number of subtle yet important differences. We attempt to bridge this gap, by adopting a minimal number of operationally motivated axioms which provide clean categorical foundations, in the style of CQM, for the treatment of the problems that OPTs are concerned with.

arXiv:1701.08075•Electronic Proceedings in Theoretical Computer Science•Feb 27, 2018•32 citations

Categories for Quantum Theory: An Introduction

Chris Heunen, Jamie Vicary

•Jan 14, 2020•32 citations

The categorical foundations of quantum information theory: Categories and the Cramer–Rao inequality

Florio M. Ciaglia, Fabio Di Cosmo, L. González-Bravo +2 more

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.

arXiv:2309.10428•Modern Physics Letters A•Jun 7, 2023•2 citations

The Foundations of Quantum Theory

Elsevier eBooks•Jan 1, 1973•45 citations
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM and OPTs have found successful application to a number of areas in quantum foundations and information theory: they present many similarities, both in spirit and in formalism, but they remain separated by a number of subtle yet important differences. We attempt to bridge this gap, by adopting a minimal number of operationally motivated axioms which provide clean categorical foundations, in the style of CQM, for the treatment of the problems that OPTs are concerned with.
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.