  We show that Coecke's compositionality theorem for quantum information flow
follows by the universal property of tensor products from the case in which all
relevant states are totally disentangled, for which the proof is almost
trivial. With the same technique we deduce a PROP structure behind general
multipartite quantum information processing and show that all such are
equivalent to a canonical teleportation-type form. Some philosophical issues
concerning quantum information are also touched upon.
