  In the context of quantum communications between two parties (here Alice and
Bob), Bob's lack of knowledge about the communications channel can affect the
purity of the states that he receives. The operation of applying an unknown
unitary transformation to a state, thus reducing its purity, is called
"twirling". As twirling affects the states that Bob receives, it also affects
his perception of the operations that Alice applies to her states. In this work
we find that not every operation is representable after a twirling, we show the
minimal requirement for this to be possible, and we identify the correct form
of the "twirled" operations.
