  Quantum hypothesis testing is an important tool for quantum information
processing. Two main strategies have been widely adopted: in a minimum error
discrimination strategy, the average error probability is minimized; while in
an unambiguous discrimination strategy, an inconclusive decision (abstention)
is allowed to vanish any possibility of errors when a conclusive result is
obtained. In both scenarios, the testing between quantum states are relatively
well-understood, for example, the ultimate limits of the performance are
established decades ago; however, the testing between quantum channels is less
understood. Although the ultimate limit of minimum error discrimination between
channels has been explored recently, the corresponding limit of unambiguous
discrimination is unknown. In this paper, we formulate an approximate
unambiguous discrimination scenario, and derive the ultimate limits of the
performance for both states and channels. In particular, in the channel case,
our lower bound of the inconclusive probability holds for arbitrary adaptive
sensing protocols. For the special class of `teleportation-covariant' channels,
the lower bound is achievable with maximum entangled inputs and no adaptive
strategy is necessary.
