# Convex and Sequential Effect Algebras. (arXiv:1802.01265v1 [quant-ph])

We present a mathematical framework for quantum mechanics in which the basic

entities and operations have physical significance. In this framework the

primitive concepts are states and effects and the resulting mathematical

structure is a convex effect algebra. We characterize the convex effect

algebras that are classical and those that are quantum mechanical. The quantum

mechanical ones are those that can be represented on a complex Hilbert space.

We next introduce the sequential product of effects to form a convex sequential

effect algebra. This product makes it possible to study conditional

probabilities and expectations.

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