We’ve supposed that is a 1-inverse of . The constants may be related by demanding that preserve the 1-norm. Let be the vector of all 1’s. Then Thus . Now a 1-inverse of satisfies . What does imposing this form for imply about ? We have , so that where , and we note that since we’ve assumed symmetric and stochastic (bistochastic) . Thus for , In particular, for , which has the form of a depolarizing channel with strength . Thus on the privileged subspace , the measure-and-prepare channel associated with the reference device simply mixes with the flat probability vector. (And if a vector has any component in , this part is projected away.) Geometrically, the channel performs an isotropic contraction of the state-space. Indeed, this is a property shared by quantum 2-designs.