Probability distributions consistent with a mixed state

A density matrix {ρ} may be represented in many different ways as a mixture of pure states, ρ=∑ᵢpᵢ|ψᵢ〉〈ψᵢ|. This paper characterizes the class of probability distributions (pᵢ) that may appear in such a decomposition, for a fixed density matrix {ρ}. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.