Generalized Quantum Stein's Lemma: Redeeming Second Law of Resource Theories

Abstract

[Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brand\~ao, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of [Bluhm, Capel, Gondolf, P\'erez-Hern\'andez, IEEE Trans. Inf. Theory 69, 5869 (2023)] used in our analysis. Due to this issue, the analysis in the previous version of this manuscript can no longer be considered complete proof of the generalized quantum Stein's lemma. This version is a temporal update to add this note. We are planning to update the manuscript further to explain the issue and what conditions we will additionally need to complete the proof of the generalized quantum Stein's lemma.]