t wt |φt 〉〈φt | represents a system which, with probability wj , is “really in” one or another of the pure states |φj 〉. In quantum mechanics, mixtures are thought to arise in two ways — as a direct mixing of distinct pure-state preparations, and “improperly” (d’Espagnat’s term), as the reduction of a pure-state composite system to the state of a component system by tracing out the other compon...