发表机构
Inner Mongolia University; Xiamen University（内蒙古大学; 厦门大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以量子比特系统的集合虚数性为量子资源，基于Bargmann不变量刻画其自由操作，构建SIMs公理化框架，提出并验证统一、完整SIMs，改进鲁棒型度量并证明其为完整SIM。
AI 中文摘要
近期研究表明，Bargmann不变量是检测集合虚数性的有效工具。本文将集合虚数性作为量子比特系统中的量子资源进行研究，通过利用Bargmann不变量的结构，证明量子比特集合虚数性的自由操作恰好包含通用幺正操作和通用平面化操作。基于该特性，我们提出了集合虚数性度量（SIMs）的公理化框架，尤其引入了统一SIMs和完整SIMs两种精细概念，可对集合虚数性进行更细粒度的量化。为使这些概念具体化，我们从三态子集的Bargmann不变量出发构建了两种量子比特SIMs，证明其中一种为统一SIM，另一种满足完整SIM的更强要求。此外，我们重新审视了文献中此前提出的集合虚数性鲁棒性，发现尽管该鲁棒性是量子比特系统中有效的SIM，但既非统一SIM也非完整SIM。为克服该局限，我们提出了一种改进的鲁棒型度量，并严格证明其可定义完整量子比特SIM。
英文摘要
Recent studies have shown that Bargmann invariants provide effective detectors of set imaginarity. In this paper, we investigate set imaginarity as a quantum resource in qubit systems. By exploiting the structure of Bargmann invariants, we show that the free operations for qubit set imaginarity consist precisely of common unital operations and common planarized operations. Based on this characterization, we introduce an axiomatic framework for set-imaginarity measures (SIMs). In particular, we propose two refined notions, namely unified SIMs and complete SIMs, which allow a more fine-grained quantification of set imaginarity. To make these notions concrete, we construct two qubit SIMs from the Bargmann invariants of three-state subsets. We prove that one of them is a unified SIM, while the other satisfies the stronger requirements of a complete SIM. Furthermore, we revisit the robustness of set imaginarity previously introduced in the literature. We show that, although this robustness is a valid SIM for qubit systems, it is neither a unified SIM nor a complete SIM. To overcome this limitation, we propose an improved robustness-type measure and rigorously prove that it defines a complete qubit SIM.
Comments13 pages, comments are welcome
Journal refPhysical Review A 114, 022453 (2026)
