Randomness cost of symmetric twirling

Abstract

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.