A Classification of Hidden-Variable Properties

Hidden-variable models of quantum mechanics (QM) are complete descriptions of quantum phenomena. These models have been analyzed under conditions such as locality (Bell [1, 1964]) and non-contextuality (Kochen-Specker [20, 1967]). We give a uniform presentation of six underlying properties that can be asked of hidden-variable models and show all the relationships among them (as depicted in Figure 1.1). Two positive existence theorems are given which show that hidden-variable models of certain types always exist. We follow this with a unified treatment of the “no-go” theorems of Einstein-Podolsky-Rosen [15, 1935], Bell [1, 1964], and Kochen-Specker [20, 1967]. Within our six-property classification scheme, we are able to give a complete picture of hidden-variable models.