Strengthen remaining vanishing-error results to fixed-error or strong-converse statements

Establish whether the remaining vanishing-error asymptotic Stein-exponent results for split-control quantum channel-discrimination games can be strengthened to fixed-error or strong-converse statements.

Background

The paper develops an achievability-to-strong-converse upgrade and applies it to selected minimax games and composite hypothesis-testing settings. However, the upgrade is not established for every vanishing-error result in the twelve-game framework. The unresolved issue is whether the remaining asymptotic exponents continue to govern performance when the type-I error is fixed, or when operation above the threshold forces the type-I error to converge to one.

References

It would also be important to determine when regularized divergences admit single-letter forms beyond replacer alternatives, and whether the remaining vanishing-error results can be strengthened to fixed-error or strong-converse statements.

— Minimax games for quantum channel discrimination  (2609.09839 - Fang et al., 9 Sep 2026) in Section 13, Section Conclusion

Further questions include the optimal strong-converse exponent, equipartition at fixed positive exponential smoothing rates, and resource-conversion rates under specified classes of superchannels.

— A Generalized Stein Lemma for Quantum Channels  (2609.30762 - Gao et al., 25 Sep 2026) in Section Discussion