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

TL;DR

This paper discusses the generalized quantum Stein's lemma within quantum resource theories, addressing recent issues in its proof and outlining future steps to establish a complete proof, thereby advancing the understanding of quantum thermodynamics.

Contribution

It revisits the generalized quantum Stein's lemma, acknowledges recent proof issues, and outlines plans for a complete proof to reinforce the second law in quantum resource theories.

Findings

Identification of issues in previous proof of the lemma

Recognition of the need for additional conditions for proof completion

Plan to develop a complete proof in future work

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.]