Extend the framework beyond classical-quantum channels

Establish a second-law framework and accompanying generalized quantum Stein’s lemma for quantum resource theories of general channels beyond the classical-quantum (measure-and-prepare) class, specifying the appropriate free operations and conditions under which asymptotic convertibility rates can be characterized by a single resource function.

Background

The paper’s channel-level second-law results are developed for CQ channels, whose Choi states have a convenient separable block-diagonal form that enables the authors’ proof techniques (including pinching and information-spectrum arguments).

Generalizing to arbitrary quantum channels with quantum inputs would likely require new techniques to handle noncommutativity and to ensure positivity/normalization in constructions analogous to those used here, making this an ambitious extension.

References

A further generalization to QRTs for channels that are not necessarily in the form of CQ channels is also left as a challenging yet interesting open problem.

— Generalized Quantum Stein's Lemma and Second Law of Quantum Resource Theories  (2408.02722 - Hayashi et al., 2024) in Methods, The second law of QRTs for states and classical-quantum (CQ) channels

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