Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *-independence is equivalent to (...) operational W *-separability. Specific further sub-types of both operational C *- and W *-separability and operational C *- and W *-independence are defined and the problem of characterization of the logical interdependencies of the independence notions is raised. (shrink)

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations, repeatability, and ideality. The problem of the operational definition of continuous observables is briefly revisited, with a special emphasis on the localization observable. Finally, a brief overview is given of possible applications of the theory to various fields and problems in quantum physics.