Probability distributions consistent with a mixed state

Abstract

A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $ρ= \sum_i p_i |ψ_i\ra \la ψ_i|$. 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.

6 pages, submitted to Physical Review A

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