Probability distributions consistent with a mixed state
Michael A. Nielsen · Physical Review A · 2000
A density matrix \ensuremath{\rho} may be represented in many different ways as a mixture of pure states, $\ensuremath{\rho}={\ensuremath{\sum}}_{i}{p}_{i}|{\ensuremath{\psi}}_{i}〉〈{\ensuremath{\psi}}_{i}|.$ This paper characterizes the class of probability distributions ${(p}_{i})$ that may appear in such a decomposition, for a fixed density matrix \ensuremath{\rho}. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.