发表机构
School of Mathematics and Statistics, Henan University; School of Mathematics Sciences, Capital Normal University（河南大学数学与统计学院; 首都师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用虚数见证算子的先验知识，推导其最大期望值的严格上界，将见证算子分为四类并分析其性质，提升了虚数检测能力，为量子虚数研究提供了理论与实验支撑。
AI 中文摘要
量子虚数是支撑现代量子技术关键功能的重要物理资源。我们借助虚数见证算子的先验知识改进虚数见证。为此，我们推导了虚数见证算子在所有自由（实）量子态集合上最大期望值的严格上界，该上界由对应见证算子实部的谱范数给出。我们通过详细实例证明，该上界显著提升了虚数检测能力。我们进一步基于此界将所有虚数见证算子分为四个不同家族。针对这四类见证，我们对其完备性、有限完备性、不同见证对共享虚数量子态的联合检测能力，以及不同见证识别相同虚数态的条件进行了全面分析。我们的结果加深了对虚数检测的基础理解，为量子虚数的理论研究和实验实现提供了有用见解。
英文摘要
Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.
