Equality of informationally degradable and (conjugate) degradable channels

Determine whether the set of informationally degradable quantum channels coincides with the union of degradable and conjugate-degradable channels, by either proving equality or constructing a counterexample.

Background

Informationally degradable channels form the largest currently known class with additive coherent information and include degradable and conjugate-degradable channels. No example is known that separates informationally degradable channels from (conjugate) degradable channels.

Resolving whether these classes are identical would clarify the scope of single-letter characterizations for quantum and private capacities.

References

It is worthwhile to point out that there is no known example of an informationally degradable channel that is not also (conjugate) degradable. It remains an interesting open problem to determine whether the two sets are identical or not.

— Approaches for approximate additivity of the Holevo information of quantum channels  (1709.01111 - Leditzky et al., 2017) in Section 6, Concluding remarks and open problems (footnote)