A density matrix rho may be represented in many different ways as a mixture
of pure states, rho = Sigma (i)p(i)\psi (i)][psi (i)\. This paper characte
rizes the class of probability distributions (p(i)) that may appear in such
a decomposition, for a fixed density matrix rho. Several illustrative appl
ications of this result to quantum mechanics and quantum information theory
are given.