Symmetry and Self-Duality in Categories of Probabilistic Models

Abstract

This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic structure of finite-dimensional quantum theory. The derivation relies on the Koecher-Vinberg Theorem, which sets up an equivalence between order-unit spaces having homogeneous, self-dual cones, and formally real Jordan algebras.

In Proceedings QPL 2011, arXiv:1210.0298

References in corpus (3)

• A derivation of quantum theory from physical requirements
• On quantum vs. classical probability
• Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models

Cited by in corpus (1)

• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories