  We show how to decompose any density matrix of the simplest binary composite
systems, whether separable or not, in terms of only product vectors. We
determine for all cases the minimal number of product vectors needed for such a
decomposition. Separable states correspond to mixing from one to four pure
product states. Inseparable states can be described as pseudomixtures of four
or five pure product states, and can be made separable by mixing them with one
or two pure product states.
