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In quantum mechanics, states can (often) be described by density matrices. That is, if $A$ is an observable, it's expected value is given by $\langle A \rangle = Tr(\rho A)$, where $\rho$ is a density matrix (or operator in the infinite dimensional case). This formulation (as opposed to using state vectors for example) has the advantage that it's easy to described so-called mixed states (i.e. non-pure states).