Optimality of repetition codes in the Du et al. advantage-distillation framework

Determine whether repetition codes provide the best noise threshold among all processing schemes in the general linear-code advantage-distillation framework of Du et al., including the framework’s additional resources and preprocessing choices.

Background

The paper studies adaptive protocols in which public messages and the candidate key are affine or linear functions of the raw keys. Its converse establishes that the covered class of adaptive linear interactions cannot surpass the six-state threshold p_*=(5−√5)/10, but the authors explicitly distinguish this result from the full framework of Du et al.

Du et al. had conjectured that repetition codes achieve the best threshold within their broader framework and had identified adaptive coding over multiple rounds as a direction for further study. Because the broader framework includes resources and preprocessing choices outside the present theorem, the optimality conjecture is not fully resolved.