  It is well-known that the action of a quantum channel on a state can be
represented, using an auxiliary space, as the partial trace of an associated
bipartite state. Recently, it was observed that for the bipartite state
associated with the optimal average input of the channel, the entanglement of
formation is simply the entropy of the reduced density matrix minus the Holevo
capacity. It is natural to ask if every bipartite state can be associated with
some channel in this way. We show that the answer is negative.
