Sharp reconstruction of unsharp quantum observables

Abstract

A well defined procedure exists which allows us to “reconstruct” a sharp, i.e., standard, quantum observable A starting from a given commutative unsharp observable F. In this work we prove that the outcomes of measurements of F can be consistently interpreted as the result of a stochastic diffusion of outcomes of its sharp reconstruction A. Furthermore, for every sharp observable B, such that F is unsharp realization of B, we explicitly construct a real mapping g such that A=g(B).