Generalize results beyond convex, finite-dimensional QRTs

Determine the extent to which the generalized quantum Stein’s lemma and the second-law characterization of asymptotic convertibility via the regularized relative entropy of resource extend beyond convex and finite-dimensional quantum resource theories whose sets of free states are closed and convex and contain a full-rank free state, including to non-convex resource theories and infinite-dimensional settings.

Background

The paper proves the generalized quantum Stein’s lemma under minimal assumptions on finite-dimensional, convex QRTs, and from it derives a second law for resource convertibility characterized by the regularized relative entropy of resource. These results cover many standard QRTs (e.g., entanglement, athermality, coherence, asymmetry, magic) in finite dimensions with convex free sets that include a full-rank state.

The authors note that modern QRTs increasingly consider non-convex free sets and infinite-dimensional systems. Extending the lemma and the second-law framework to such cases would broaden applicability substantially but requires overcoming technical obstacles (e.g., compactness, continuity, tensor-product structure) that their present proof relies on.