  Two quantum channels are called compatible if they can be obtained as
marginals from a single broadcasting channel; otherwise they are incompatible.
We derive a characterization of the compatibility relation in terms of
concatenation and conjugation, and we show that all pairs of sufficiently noisy
quantum channels are compatible. The complement relation of incompatibility can
be seen as a unifying aspect for many quantum features. We demonstrate that
several phenomena, such as impossibility of universal broadcasting and
unavoidable measurement disturbance, appear naturally in this framework.
