The Einstein-Podolsky-Rosen (EPR) reality criterion is generalized to fit with the notion of positive-operator-valued observables occurring in quantum optics, stochastic quantum mechanics, and other fields of quantum physics. The resulting concept of unsharp reality for quantum systems is illustrated within stochastic spin space where it leads to a notion of unsharp spin property. Finally we investigate the possibility of joint spin measurements and give a brief discussion of the EPR-Bell argument for unsharp spin properties.

• Received 21 October 1985

DOI:https://doi.org/10.1103/PhysRevD.33.2253