States, Effects and Observables

Abstract

In this chapter we review the basic elements and structures of Hilbert space quantum mechanics. We build on the idea of a statistical duality arising from the analysis of an experiment as a preparation-measurement-registration scheme, as sketched in Sect. 1.2. The description of a physical system SS is thus based on the notions of states as equivalence classes of preparations, observables as equivalence classes of measurements, and on the probability measures for the possible measurement outcomes.