Given two sets of quantum states, is it possible to transform one to the other by a quantum channel? This question has been studied by many authors and recently fully settled by a set of entropic inequalities. We will consider an extension of this problem that can be formulated as follows: given two bipartite quantum channels, how precisely can one be approximated by applying a suitable supermap to a part of the other? Taking some inspiration from the classical randomization criterion by Le Cam, we study this question it the case when the precision of the approximation is measured by distance in the diamond norm.