Asymptotic conversion rates for the resource theory of superposition

Evaluate the asymptotic rates of reversible resource conversion for many-copy superposition under the resource theory of superposition with product reference states.

Background

The paper notes that, for many copies with product reference states, the free sets satisfy the structural assumptions of the reversible resource-theory framework of Brandão and Gour, including closure under tensor products, partial traces, and permutations and containment of a full-rank state. Although the generalized quantum Stein's lemma needed by that framework has recently been established, the resulting asymptotic conversion rates for the resource theory of superposition have not yet been determined.

References

For many copies, with product reference states, the free sets of the RTS are closed under tensor products, partial traces, and permutations and contain a full-rank state, so they satisfy the axioms of the reversible framework of Ref., whose key ingredient, the generalized quantum Stein's lemma, has recently been established; the resulting asymptotic rates remain to be evaluated for the RTS.

— Majorization for superpositions of nonorthogonal states and the existence of golden states  (2610.26483 - Torun, 19 Oct 2026) in Section Conclusion