  We show a lower bound on expected communication cost of interactive
entanglement assisted quantum state redistribution protocols and a slightly
better lower bound for its special case, quantum state transfer. Our bound
implies that the expected communication cost of interactive protocols is not
significantly better than worst case communication cost, in terms of scaling of
error. Furthermore, the bound is independent of the number of rounds. This is
in contrast with the classical case, where protocols with expected
communication cost significantly better than worst case communication cost are
known.
