Universal private-capacity superactivation by antidegradable partners

Establish whether every transpose-antidegradable channel that is not antidegradable admits an antidegradable partner channel that produces positive private capacity when used jointly, namely whether for every such channel \(\mathcal N\) there exists an antidegradable channel \(\mathcal A\) satisfying \(P(\mathcal N\otimes\mathcal A)>0\).

Background

The paper demonstrates that its specific transpose-antidegradable channel $\mathcal F$, which is not antidegradable, superactivates private capacity when combined with the antidegradable channel $\mathcal G$. It also notes that an independent construction exhibits the same behavior.

This motivates the broader unresolved question of whether private-capacity superactivation is a general consequence of the separation between transpose antidegradability and antidegradability, rather than a property limited to particular channel constructions.