  To decide whether a quantum channel is degradable is relatively easy: one has
to find at least one example of a degrading quantum channel. But in general, no
conclusive criterion exists to show the opposite. Using elementary methods we
derive a necessary and sufficient condition to decide under what circumstances
the conclusion is unambiguous. The findings lead to an extension of the
antidegradability region for qubit and qutrit transpose depolarizing channels.
In the qubit case we reproduce the known results for the class of qubit
depolarizing channels (due to their equivalence). One of the consequences is
that the optimal qubit and qutrit asymmetric cloners possess a single-letter
quantum capacity formula. We also investigate the ramifications of the
criterion for the search of exclusively conjugate degradable channels.
