Probability distributions consistent with a mixed state

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 characterizes the class of probability distributions (p(i)) that may appear in such a decomposition, for a fixed density matrix rho. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.