"Pretty strong" converse for the quantum capacity of degradable channels

Understand

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.