A structure for quantum measurements

This paper presents an additive and product structure for quantum measurements. The additive structure generalizes the orthosum of effects in effect algebras and preserves sums of expectations. The additive structure also provides a natural order for measurements and it is shown that an initial interval of measurements forms an effect algebra. In certain cases, this effect algebra retains the properties of the original effect algebra on which the measurements are defined. Various sequential products of measurements are introduced and compared. Conditional measurements are also studied.