Combined systems in quantum probability
A framework for quantum probability is developed, that is based on ideas of Feynman probability amplitudes, and different notions of combination of systems are studied within this framework. In particular, the horizontal sum, the direct sum and the Cartesian product of quantum probability systems are studied. The concepts of interference and independence of measurements relative to an amplitude density are introduced, and manifestations of these concepts for the various combinations are studied. Superpositions of amplitude densities are also considered, that result in unnormalized amplitudes, and the maximal superposition sets of amplitudes, called sectors, are distinguished. The superselection sector structures are explained first on finite quantum probability models and then elaborated in full generality.
scientific article; zbMATH DE number 4215027