Mechanism behind minimum-output-entropy nonadditivity

Identify a transparent mathematical mechanism explaining why quantum channels exhibit nonadditivity of minimum output entropy beyond the concentration-of-measure argument establishing existence.

Background

The paper distinguishes the known existence of finite-dimensional counterexamples from the unresolved task of explaining the phenomenon structurally. Although the paper develops a free-probabilistic and permutation-based framework, it does not claim that this fully identifies a transparent underlying mechanism for nonadditivity.

References

Thus, in this particular case, the entropy-reducing effect of weakening neurons is due to an indirect and cumulative effect. More fully understanding the mechanisms behind this is left to future work.

— Weakening Neurons: An Input-Output Functionality in Transformers with Outsize Influence  (2609.18612 - Gerstner et al., 16 Sep 2026) in Section 4.3, Case study of entropy reduction

identifying a transparent mathematical mechanism behind nonadditivity (which is quite open).

— Superadditivity of classical communication over quantum channels via random and deterministic permutations  (2608.25961 - Lovitz et al., 26 Aug 2026) in Acknowledgments and Disclosure of AI usage