Finite-Dimensional Convex Effect Algebras

Abstract

We first show that the convex effect algebras (CEA) approach to quantum mechanics is more general than the general probabilistic theories approach. We then restrict our attention to finite-dimension CEA's. After an introductory Section~1, we present basic definitions in Section~2. Section~3 studies convex subeffect algebras and observables. In Section~4 we consider strong CEA's and strong observables. We show that a CEA is strong if and only if it is classical. Informationally complete observables on classical CEA's are studied in Section~5. Section~6 considers quantum CEA's in Hilbert spaces.