General probabilistic theories: An introduction

TL;DR

This paper introduces the framework of general probabilistic theories (GPTs), which unify classical, quantum, and exotic operational theories using convex geometry and diagrammatic notation, providing foundational insights into their structure.

Contribution

It offers a comprehensive, self-contained introduction to GPTs, including key concepts, results, and tools like convex geometry and diagrammatic notation, for the first time.

Findings

Unified framework for classical, quantum, and exotic theories

Proved several well-known results within GPTs

Developed diagrammatic notation for operational theories

Abstract

We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories, such as the boxworld theory containing Popescu-Rohrlich boxes. We provide in-depth explanations of the basic concepts and elements of the framework of GPTs, and we also prove several well-known results. The review is self-contained and it is meant to provide the reader with consistent introduction to GPTs. Our tools mainly include convex geometry, but we also introduce diagrammatic notation and we often express equations via diagrams.