Post-Classical Probability Theory

TL;DR

This paper introduces the framework of general probabilistic theories to better understand quantum mechanics as a generalization of classical probability, reviewing key phenomena and recent structural derivations.

Contribution

It provides an overview of the convex-operational approach and discusses recent derivations of quantum structures from operational postulates.

Findings

Quantum phenomena like cloning, teleportation, and entanglement fit within the general probabilistic framework.

Recent derivations show the Jordan-algebraic structure of quantum theory from operational principles.

Abstract

This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is to locate quantum mechanics within a very much more general, but conceptually very straightforward, generalization of classical probability theory. The hope is that, by viewing quantum mechanics "from the outside", we may be able better to understand it. We illustrate several respects in which this has proved to be the case, reviewing work on cloning and broadcasting, teleportation and entanglement swapping, key distribution, and ensemble steering in this general framework. We also discuss a recent derivation of the Jordan-algebraic structure of finite-dimensional quantum theory from operationally reasonable postulates.