发表机构
Universidad Nacional Autónoma de México; Universidad Nacional de Colombia; Universidade Federal de Pernambuco（墨西哥国立自治大学; 哥伦比亚国立大学; 伯南布哥联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推进量子态纹理资源理论，通过总和刻画自由操作、分类纹理蒸馏并引入集合纹理，为QST应用奠定基础。
AI 中文摘要
最近引入的量子态纹理（QST）概念已在从未知量子门的识别到量子相变和临界性的研究等多个领域得到应用，并且已经得到了实验研究。在此，我们在多个方向上推进其资源理论形式化。我们的方法集中于实验上可访问的总和——即密度算符在给定基下的所有矩阵元素之和。我们澄清了近期文献中提出的几个问题，包括纹理蒸馏与基于总和的简单QST单调量之间的关系。我们完全刻画了单量子比特的自由操作，并研究了由此产生的态转换序；在任意维度下对相关自由操作族进行了分类；推导了复合系统纹理与其子系统纹理之间的界限；并引入了与基无关的集合纹理概念。这些结果共同加强并拓宽了QST的资源理论，为其进一步发展和应用奠定了基础。
英文摘要
The recently introduced concept of quantum-state texture (QST) has found applications ranging from the identification of unknown quantum gates to the study of quantum phase transitions and criticality, and has already been experimentally investigated. Here, we advance its resource-theoretic formulation in several directions. Our approach centers on the experimentally accessible grand sum--the sum of all matrix elements of a density operator in a given basis. We clarify several points raised in the recent literature, including the relation between texture distillation and a simple grand-sum-based QST monotone. We completely characterize free operations for a single qubit and study the resulting state-conversion order; classify relevant families of free operations in arbitrary dimensions; derive bounds relating the texture of composite systems to that of their subsystems; and introduce the basis-independent concept of set texture. Together, these results strengthen and broaden the resource theory of QST, providing a foundation for its further development and applications.
Comments29 pages; 22+5 pages excluding references; 2 figures
