[论文解读] Resource-Theoretic Quantifiers of Weak and Strong Symmetry Breaking: Strong Entanglement Asymmetry and Beyond

Yuya Kusuki, Sridip Pal+1 more|arXiv (Cornell University)|Jan 28, 2026

Quantum many-body systems被引用 0

一句话总结

该论文为强对称性破缺建立了一套资源理论框架，扩展了纠缠不对称性，并识别出区分开放量子系统中强对称性与弱对称性的量纲，在 U(1) 的情况下，方差能够完全表征宏观强对称性破缺。

ABSTRACT

Quantifying how much a quantum state breaks a symmetry is essential for characterizing phases, nonequilibrium dynamics, and open-system behavior. Quantum resource theory provides a rigorous operational framework to define and characterize such quantifiers of symmetry-breaking. As a starter, we exemplify the usefulness of resource theory by noting that second-Rényi entanglement asymmetry can increase under symmetric operations, and hence is not a resource monotone, and should not solely be used to capture Quantum Mpemba effect. More importantly, motivated by mixed-state physics where weak and strong symmetries are inequivalent, we formulate a new resource theory tailored to strong symmetry, identifying free states and strong-covariant operations. This framework systematically identifies quantifiers of strong symmetry breaking for a broad class of symmetry groups, including a strong entanglement asymmetry. A particularly transparent structure emerges for U(1) symmetry, where the resource theory for the strong symmetry breaking has a completely parallel structure to the entanglement theory: the variance of the conserved quantity fully characterizes the asymptotic manipulation of strong symmetry breaking. By connecting this result to the knowledge of the geometry of quantum state space, we obtain a quantitative framework to track how weak symmetry breaking is irreversibly converted into strong symmetry breaking in open quantum systems. We further propose extensions to generalized symmetries and illustrate the qualitative impact of strong symmetry breaking in analytically tractable QFT examples and applications.

研究动机与目标

• 为量化超越弱对称性的对称性破缺提供资源理论方法的动机与形式化
• 为强对称性资源理论定义自由态与自由操作
• 识别并验证作为强对称性破缺量度的单调量，在自由操作下保持单调
• 显示强对称量度可扩展到广义对称性，并与态-空间几何相关

提出的方法

• 回顾对称性资源理论及其与相对熵的关系（相对熵的不对称性）
• 引入针对强对称性的新资源理论，给出自由态与自由操作
• 提出新的强对称性量度，包括基于方差的测量和基于协方差矩阵的量
• 在 U(1) 的特化中，守恒量的方差支配强对称性破缺的渐近蒸馏与稀释
• 通过单一区段态将框架推广到广义对称性与非阿贝尔群
• 将量度与量子态空间几何与信息几何度量联系起来

Figure 1: Classifications of states. In the figure, asymmetric states are indicated by the hatched region, whereas symmetric states are shown as the three shaded regions. The set of symmetric states exhibits a three-level nested hierarchical structure, i.e. (strong symmetric) $\subset$ (single-secto

实验结果

研究问题

• RQ1 如何在资源理论框架内 formalize 强对称性破缺？
• RQ2 哪些自由态与自由操作能够捕捉强对称性，哪些单调量可用于量化强对称性破缺？
• RQ3 强对称性量化如何与弱对称性相关，是否能区分具有相同弱对称性属性的态？
• RQ4 在量化强对称性破缺中，尤其是对 U(1)，守恒量的方差起到怎样的作用？
• RQ5 框架能否扩展到广义与非阿贝尔对称性并与态空间几何相联系？

主要发现

• 一个具有一致自由态与协变自由操作的强对称性资源理论是可构建的。
• 提出新的强对称性量度并证明它们是资源单调量。
• 对于 U(1) 对称性，守恒量的方差完全表征强对称性破缺的渐近操作。
• Second Rényi 对称性不再被视为对称性操作下的真正单调量。
• 该框架在混合态中区分了强对称性破缺，超出弱对称性测度的覆盖范围。
• 并讨论对广义对称性的扩展及对开放系统动力学的定性应用。

Figure 2: Schematic diagram of physical realization of operations that are strong covariant with respect to particle number and weak covariant with respect to energy. The system exchanges energy with an external heat bath, while no particles are exchanged.