  I consider the problem of deterministically distinguishing the state of a
multipartite system, from a set of $N\ge d+1$ orthogonal states, where $d$ is
the dimension of each party's subsystem. It is shown that if the set of
orthogonal states is chosen at random, then there is a vanishing probability
that this set will be perfectly distinguishable under the restriction that the
parties use only local operations on their subsystems and classical
communication amongst themselves.
