  A given density matrix may be represented in many ways as a mixture of pure
states. We show how any density matrix may be realized as a uniform ensemble.
It has been conjectured that one may realize all probability distributions that
are majorized by the vector of eigenvalues of the density matrix. We show that
if the states in the ensemble are assumed to be distinct then it is not true,
but a marginally weaker statement may still be true.
