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

TL;DR

This paper demonstrates a 'pretty strong' converse property for the quantum capacity of degradable channels, showing a discontinuous fidelity jump at the capacity threshold, and links it to the strong converse for symmetric channels.

Contribution

It introduces the 'pretty strong' converse for degradable channels and connects it to the strong converse for symmetric channels, advancing understanding of quantum capacity limits.

Findings

Fidelity drops from 1 to at most 0.707 when exceeding quantum capacity.

Similar results apply to private (classical) capacity.

If the strong converse holds for symmetric channels, it extends to degradable channels.

Abstract

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.