  Unambiguous unitary maps and unambiguous unitary quantum channels are
introduced and some of their properties are derived. These properties ensure
certain simple form for the measurements involved in realizing an unambiguous
unitary quantum channel. Error correction and unambiguous error correction with
nonzero probability are discussed in terms of unambiguous unitary quantum
channels. We not only re-derive the well-known condition for a set of errors to
be correctable with certainty, but also obtain a necessary and sufficient
condition for the errors caused by a noisy channel to be correctable with any
nonzero probability. Dense coding with a partially entangled state can also be
viewed as an unambiguous unitary quantum channel when all messages are required
to be transmitted with equal probability of success, the maximal achievable
probability of success is derived and the optimum protocol is also obtained.
