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arXiv · 1912.05110

Finite-Dimensional Convex Effect Algebras

Stan Gudder
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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.

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Stan Gudder. 2019-12-11. Finite-Dimensional Convex Effect Algebras. https://arxiv.org/abs/1912.05110

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