标题： 投影测量的相干性度量的保序条件及一个示例 显示英文标题

标题： Order-preserving condition for coherence measures of projective measurements with One Example

摘要： 叠加是量子力学的一个基本特征。 从薛定谔的猫到量子算法如Deutsch-Jozsa算法，量子叠加起着重要作用。 如何量化叠加是一个基本且关键的问题。 到目前为止，相干性的框架已经被很好地建立为量子资源理论的一个典型实例。 并且，相干性的概念已经被推广到线性无关基、投影测量和POVMs中。 在本工作中，我们将关注针对投影测量或正交子空间的相干性度量。 提出了一个新的条件，即保序条件，用于此类度量。 这一条件根植于希尔伯特空间正交分解的数学结构。 并通过将相干性的1/2相似度推广到子空间情况，我们验证了这种广义的相干性度量满足保序条件。 它还满足其他合理的条件，以成为一种好的相干性度量。 由于偏序关系不仅存在于投影测量中，也存在于POVM中，因此自然地研究POVM情况下的保序条件，这将是本工作的最后一部分。 显示英文摘要

摘要： Superposition is an essential feature of quantum mechanics. From the Schrodinger's cat to quantum algorithms such as Deutsch-Jorsza algorithm, quantum superposition plays an important role. It is one fundamental and crucial question how to quantify superposition. Until now, the framework of coherence has been well established as one typical instance of quantum resource theories. And the concept of coherence has been generalized into linearly independent basis, projective measurements and POVMs. In this work, we will focus on coherence measures for projective measurements or orthogonal subspaces. One new condition, order-preserving condition, is proposed for such measures. This condition is rooted in the mathematical structure of Hilbert spaces' orthogonal decomposition. And by generalizing the 1/2-affinity of coherence into subspace cases, we verify that this generalized coherence measure satisfies the order-preserving condition. And it also satisfies other reasonable conditions to be a good coherence measure. As the partial order relationship exists for not only projective measurements, but also POVMs, it's natural to study the order-preserving condition in POVM cases, which will be the last part of this work.