发表机构
Institute for Advanced Study, Kyushu University; Department of Physics, Kyushu University; RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS); Department of Informatics, Faculty of Information Science and Electrical Engineering, Kyushu University; Japan Science and Technology Agency (JST), FOREST; Department of Engineering Science, Graduate School of Informatics and Engineering, The University of Electro-Communications（九州大学先进研究院; 九州大学物理系; 理化学研究所交叉理论与数学科学中心（iTHEMS）; 九州大学信息科学与电气工程学院信息学系; 日本科学技术振兴机构（JST）FOREST计划; 电波大学信息与工程学院工程科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明完备性对探测对称性破缺至关重要，提出基于保真度的对数特征函数扩展，优于纠缠不对称性，可区分弛豫动力学并识别离散对称性Mpemba效应。
AI 中文摘要
完备性在量子信息中被广泛认为是单调量族的一个重要性质，因为它确保不会丢失与态转换相关的信息。我们证明完备性在多体系统中也具有物理重要性：一个不完备的对称性破缺度量可能会遗漏对称性恢复动力学的关键特征。我们研究了对数特征函数（LCF），也称为弦序参量，其完整族对于有限群在对称性保持操作下的精确独立同分布纯态转换是完备的。我们将基于保真度的LCF扩展至混合态，并确定了相对于纠缠不对称性（EA）的两个具体优势。首先，对于有限对称群$G$，EA受$\u001c\log |G|$限制，并且在热力学极限下，不同初始态可能趋近于相同的饱和值，使得它们的弛豫曲线无法区分，从而阻碍了对离散对称性Mpemba效应的识别。相比之下，LCF可以保持广延性，其系数依赖于初始态和时间，因此能继续区分它们的弛豫动力学。其次，不同的LCF分量可以表现出不同的弛豫和交叉行为，包括EA不显示交叉的情况。我们在自旋链淬火和单量子比特系统在退极化噪声下的动力学中展示了这些优势。我们还为量子场论中基于保真度的LCF开发了复制构造，并推导了共形场论的解析结果。
英文摘要
Completeness is widely recognized in quantum information as an important property of a family of monotones, because it ensures that no information relevant to state conversion is lost. We show that completeness is also physically important in many-body systems: an incomplete measure of symmetry breaking can miss essential features of symmetry-restoration dynamics. We study the logarithmic characteristic function (LCF), also known as the string order parameter, whose full family is complete for exact i.i.d. pure-state conversion under symmetry-preserving operations for finite groups. We introduce a fidelity-based extension of the LCF to mixed states and identify two concrete advantages over entanglement asymmetry (EA). First, for a finite symmetry group $G$, EA is bounded by $\log |G|$ and can approach the same saturated value for different initial states in the thermodynamic limit, making their relaxation curves indistinguishable and preventing the identification of a discrete-symmetry Mpemba effect. By contrast, the LCF can remain extensive, with a coefficient that depends on the initial state and time, and therefore continues to distinguish their relaxation dynamics. Second, different LCF components can exhibit distinct relaxation and crossing behavior, including cases in which EA shows no crossing. We demonstrate these advantages in spin-chain quenches and a single-qubit system under depolarizing noise. We also develop a replica construction for the fidelity-based LCF in quantum field theory and derive analytical results for conformal field theory.
Comments42 pages, 7 figures
