Sharp and Unsharp Quantum Effects

AbstractA survey of the algebraic and the statistical properties of sharp and unsharp quantum effects is presented. We begin with a discussion and a comparison of four types of probability theories, the sharp and unsharp classical and quantum theories. A structure called an effect algebra that generalizes and unifies all four of these probability theories, is then considered. Finally, we present some recent investigations on tensor products and quotients of effect algebras. Examples and representative results for the various theories are discussed