Discrete Generalized Observables and Ideal Measurements in the ESR Model: A Hilbert Space Representation

The extended semantic realism (ESR) model embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the discrete generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection Postulate and suggest a possible mathematical description of an ideal measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.