  Entanglement distribution with separable states has recently attracted
considerable attention. Recent results suggest that quantum discord - a measure
for quantum correlations beyond entanglement - is responsible for this
counterintuitive phenomenon. In this work we study this question from a
different perspective, and find minimal requirements for a separable state to
be useful for entanglement distribution. Surprisingly, we find that the
presence of quantum discord is not sufficient to ensure entanglement
distribution: there exist states with nonzero quantum discord which
nevertheless cannot be used for entanglement distribution. As a result, we show
that entanglement distribution is not possible with rank two separable states.
Our work sheds new light on the task of entanglement distribution with
separable states, and reveals a new classification of quantum states with
respect to their usefulness for this task.
