  For a pair of quantum channels with the same input space, we show that the
possibility of approximation of one channel by post-processings of the other
channel can be characterized by comparing the success probabilities for the two
ensembles obtained as outputs for any ensemble on the input space coupled with
an ancilla. This provides an operational interpretation to a natural extension
of Le Cam's deficiency to quantum channels. In particular, we obtain a version
of the randomization criterion for quantum statistical experiments. The proofs
are based on some properties of the diamond norm and its dual, which are of
independent interest.
