  We show that several classes of mixed quantum states in finite-dimensional
Hilbert spaces which can be characterized as being, in some respect, 'most
classical' can be described and analyzed in a unified way. Among the states we
consider are separable states of distinguishable particles, uncorrelated states
of indistinguishable fermions and bosons, as well as mixed spin states
decomposable into probabilistic mixtures of pure coherent states. The latter
were the subject of the recent paper by Giraud et. al., who showed that in the
lowest-dimensional, nontrivial case of spin 1, each such state can be
decomposed into a mixture of eight pure states. Using our method we prove that
in fact four pure states always suffice.
