Probabilistic models of quantum systems, and Bell type inequalities (Q1420656)

It is shown that each quantum system may be associated with a measurable space \((\Omega, \mathcal B_{\Omega}\) and a mapping \(F_1\) of the set of observables of this system to the set of measurable functions on \(\Omega\) as well as a mapping \(F_2\) of the set of system states to the set of probabilistic measures on \((\Omega, \mathcal B_{\Omega}\). The distribution of simultaneous observations of pairwise commutating values coincides with the common distribution of random values. This is true for an arbitrary state of the quantum system and for a finite set of pairwise commutating values.