DIFFERENCE POSETS, EFFECTS, AND QUANTUM MEASUREMENTS

Difference posets as generalizations of quantum logics, orthoalgebras, and effects are studied. Observables and measures generalizing normalized POV-measures and generalized measures on sets of effects are introduced. Characterization of orthomodularity of subsets of a difference poset in terms of triangle closedness and regularity of these subsets enables us to characterize observables with a Boolean range. Boolean powers of difference posets are investigated; they have similar properties to that of tensor products, and their connection with quantum measurements is studied.