"Classical" quantum states

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 was the subject of the recent paper by Giraud et al. [Phys. Rev. A 78, 042112 (2008)], 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.