Randomness cost of symmetric twirling

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