论文标题
基于体重的相干度量和混合最大相干状态的异常
Anomalies of weight-based coherence measure and mixed maximally coherent states
论文作者
论文摘要
作为纠缠理论框架中最佳可分离近似（BSA）的类比，在这里，我们集中于最佳不一致近似的概念，并应用于表征和量化量子相干性。从分析和数值的角度来看，我们已经证明了基于重量的连贯性测量表现出与其他流行相干量化器形成鲜明对比的一些异常特性。首先，通过得出量子状态的封闭公式，我们显示了基于重量的相干度量，即使在这种最简单的情况下，也表现出丰富的（几何）结构。其次，我们已经确定了相对于这种相干度量的混合最大相干状态（MMC）的存在，并讨论了MMC在高维希尔伯特空间中的特征。特别是，我们通过从数值模拟中获得见解来介绍几个重要的MMC系列。此外，还指出，这项工作中的某些考虑因素可以推广到一般凸资源理论，并讨论了提高查找BSA的计算效率的数值方法。
As an analogy of best separable approximation (BSA) in the framework of entanglement theory, here we concentrate on the notion of best incoherent approximation, with application to characterizing and quantifying quantum coherence. From both analytical and numerical perspectives, we have demonstrated that the weight-based coherence measure displays some unusual properties, in sharp contrast to other popular coherence quantifiers. First, by deriving a closed formula for qubit states, we have showed the weight-based coherence measure exhibits a rich (geometrical) structure even in this simplest case. Second, we have identified the existence of mixed maximally coherent states (MMCS) with respect to this coherence measure and discussed the characteristic feature of MMCS in high-dimensional Hilbert spaces. Especially, we present several important families of MMCS by gaining insights from the numerical simulations. Moreover, it is pointed out that some considerations in this work can be generalized to general convex resource theories and a numerical method of improving the computational efficiency for finding the BSA is also discussed.
