  We study random unitary channels which reproduce the action of the twirling
channel corresponding to the representation of the symmetric groupon an n-fold
tensor product. We derive upper andlower bounds on the randomness cost of
implementing such a map which depend exponentially on the number of systems.
Consequently, symmetrictwirling can be regarded as a reasonable Shannon
theoretic protocol. On the other hand, such protocols are disqualified by their
resource-inefficiency in situations where randomness is a costly resource.
