Categorical Probabilistic Theories

TL;DR

This paper introduces a categorical framework that unifies and bridges the gap between Categorical Quantum Mechanics and Operational Probabilistic Theories, facilitating their application in quantum foundations and information theory.

Contribution

It provides a minimal axiomatic, categorical foundation that reconciles the differences between CQM and OPTs, enabling integrated analysis.

Findings

Unified categorical framework for probabilistic theories

Reconciliation of CQM and OPTs with minimal axioms

Enhanced applicability to quantum foundations and information theory

Abstract

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.