  In quantum mechanics, outcomes of measurements on a state have a
probabilistic interpretation while the evolution of the state is treated
deterministically. Here we show that one can also treat the evolution as being
probabilistic in nature and one can measure `which unitary' happened. Likewise,
one can give an information-theoretic interpretation to evolutions by defining
the entropy of a completely positive map. This entropy gives the rate at which
the informational content of the evolution can be compressed. One cannot
compress this information and still have the evolution act on an unknown state,
but we demonstrate a general scheme to do so probabilistically. This allows one
to generalize super-dense coding to the sending of quantum information. One can
also define the ``interaction-entanglement'' of a unitary, and concentrate this
entanglement.
