2012/10/02 by Alexander Wilce
Physics and Astronomy · Computer Science · Mathematics · #math-ph #cs.LO #math.MP #quant-ph
paper · pdf · doi:10.4204/eptcs.95.19
published as EPTCS 95, 2012, pp. 275-279 · In Proceedings QPL 2011, arXiv:1210.0298
arxiv created 2012/10/02 · arxiv updated 2012/10/03
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.