ABSTRACT
Most of the predictions of quantum mechanics are of a statistical nature and therefore make sense only for ensembles. The axiomatics based on the quantum calculus of propositions might open the way toward a general definition of the quantum state of an individual system. It was soon recognized that this leads to separability and thereby to violation of some of the quantum-mechanical predictions. In contemporary literature, the concept of state is not wholly unambiguous. Some authors associate it with the notion of an individual system and say, for instance that a given system is in a given state. Others associate it exclusively with ensembles. The situation is complicated by the fact that for some theorists the concept of state refers only to ensembles that can be described by some state vector. For other authors it refers just as well to ensembles that cannot be associated with any state vector and for which only a density matrix description is therefore acceptable.
