What are the observable effects of the physical properties of a quantum system?

In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of a quantum system. We find that the values of physical properties are determined by the combination of initial and final conditions, which means that eigenstates and eigenvalues should not be misinterpreted as an exclusive set of possible realities. Here, we discuss the practical implications of these results and point out the importance of quantitative relations for a proper understanding of physical effects.