On the Non-Unique Decomposability of Quantum Mixtures

Abstract

In the Hilbert space formulation of quantum mechanics the set of pure states of a physical system is rich enough to generate, by convex combination, the set of all non-pure states (or mixtures). But it is a well-known fact that the knowledge of a non-pure state does not determine uniquely the pure states of which it is a convex combination. In the sequel we shall often refer to that as the non-unique decomposability of mixtures. The following items might outline the situation as it appears in Hilbert space quantum mechanics.