近日，日本东京大学Yamasaki, Hayata团队联合香港中文大学（深圳）深圳国际量子研究院Hayashi, Masahito团队研究了广义量子Stein引理与量子资源理论第二定律。2025年10月29日出版的《自然—物理学》杂志发表了这项成果。

热力学第二定律是物理学中的一个基本概念，它通过一个单一的函数——熵来描述热力学状态之间的可转换性。量子信息理论中的一个重要问题是是否可以为量子信息处理中的资源（如纠缠）建立类似的第二定律。2008年，有人提出了一个公式，将电阻可兑换性与量子版本假设检验的一种变体的最佳性能联系起来。该建议以广义量子斯坦引理为主题，通过测量量子资源，即正则化的相对熵来表征这种最优性能。如果这种方法是有效的，则可以建立量子资源的第二定律，其中正则化的相对熵扮演热力学熵的角色。然而，在2023年，在广义斯坦因引理的证明中发现了一个空白。

研究组在一个较小的假设集合下提供广义量子斯坦引理的另一种证明。此外，研究组重新建立和扩展了量子抵抗理论第二定律，它既适用于量子态的静态抵抗，也适用于以经典量子通道为代表的动态抵抗。

附：英文原文

Title: The generalized quantum Stein’s lemma and the second law of quantum resource theories

Author: Hayashi, Masahito, Yamasaki, Hayata

Issue&Volume: 2025-10-29

Abstract: The second law of thermodynamics is a fundamental concept in physics, characterizing the convertibility between thermodynamic states through a single function—entropy. An important question in quantum information theory has been whether an analogous second law can be established for resources in quantum information processing, such as entanglement. In 2008, a formulation was proposed, linking resource convertibility to the optimal performance of a variant of the quantum version of hypothesis testing. The proposal made use of the generalized quantum Stein’s lemma to characterize this optimal performance by a measure of quantum resources, the regularized relative entropy of resource. If this approach is valid, a second law for quantum resources can be established, with the regularized relative entropy of resource taking on the role of thermodynamic entropy. However, in 2023, a gap was found in the proof of the generalized Stein’s lemma. Here we provide an alternative proof of the generalized quantum Stein’s lemma under a smaller set of assumptions. Furthermore, we re-establish and extend the second law of quantum resource theories, applicable to both static resources of quantum states and dynamical resources represented by classical–quantum channels.

DOI: 10.1038/s41567-025-03047-9

Source: https://www.nature.com/articles/s41567-025-03047-9