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.