Partial-state formalism and the object-subject split in quantum mechanics

A suitable general statistical framework is established by taking quantum mechanics as full, and other (state-distinguishing) statistical theories as partial theories with respect to a given relevant subset of observables. The partial theory exists and is unique up to equivalence. The choice of the simplest or canonical one is determined. The recently introduced hybrid, i.e., half quantum mechanical and half classical discrete, statistical states obtain thus their rightful place in a hierarchy of relevant quantum statistical theories. On the other hand, these states are shown to represent a derivation of the quantum object-subject split with a well-defined subject that encompasses preparator or measuring instrument in a natural way.