After decoherence, only states A or B can be observed, not any superposition of them. Nevertheless, the quantum-to-classical transition is not complete yet in standard quantum mechanics. Decoherence leaves the subsystem in an improper mixture, which still implies that the subsystem may be in either state while we only actually observe one of the states. Thus, one more step is needed to complete the transition, which is the collapse. For the two-state example in Figure , the collapse would definitely bring the system to either state A or B. If one considers an ensemble of identically prepared subsystems, it yields a proper mixture. Although the figure is restricted to the system (as the index S indicates), collapse extends over the entire density matrix, including apparatus, environment, observer, and, in the limit, the universe.