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.

翻译：我们研究随机单一频道,这些频道复制与对称组的表示相对应的旋转频道的动作,我们从执行这种地图的随机性成本中获得上下限,这种随机性成本指数取决于系统的数量。因此,对称性旋转可被视为合理的香农理论协议。另一方面,在随机性是一个昂贵资源的情况下,这种协议因其资源效率低下而被取消资格。