Symmetry and Self-Duality in Categories of Probabilistic Models
Mathematical Physics
2012-10-03 v1 Logic in Computer Science
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1210.0622,
title = {Symmetry and Self-Duality in Categories of Probabilistic Models},
author = {Alexander Wilce},
journal= {arXiv preprint arXiv:1210.0622},
year = {2012}
}
Comments
In Proceedings QPL 2011, arXiv:1210.0298