  We exhibit a possible road towards a strong converse for the quantum capacity
of degradable channels. In particular, we show that all degradable channels
obey what we call a "pretty strong" converse: When the code rate increases
above the quantum capacity, the fidelity makes a discontinuous jump from 1 to
at most 0.707, asymptotically. A similar result can be shown for the private
(classical) capacity. Furthermore, we can show that if the strong converse
holds for symmetric channels (which have quantum capacity zero), then
degradable channels obey the strong converse: The above-mentioned asymptotic
jump of the fidelity at the quantum capacity is then from 1 down to 0.
