Abstract
A quantum mechanical system that is described by a state vector can be equally described by a density operator, although the inverse is not true. When information about a system is incomplete the only way to describe the system is by the density operator formalism. Incompleteness arises in two general cases: a mixed ensemble of physical systems and a system that interacts with its environment. We shed light on some subtle points that are usually misunderstood. We show explicitly that in the first case the averaged state vector of the system is zero, and in the second case no state vector can be assigned to the system in general.
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