Coherence measures based on coherence eigenvalue and their applications
Coherence measures based on coherence eigenvalue and their applications
复制标题
基于相干特征值的相干性测度及其应用
DOI：
10.1007/s11128-019-2461-9
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发表时间：
2019
影响因子：
2.5
通讯作者：
Li Ming
中科院分区：
文献类型：
--
作者：
Li Lei;Wang Qing Wen;Shen Shu Qian;Li Ming
相干性的量化是量子信息理论的核心，但还远未被完全理解，特别是对于多体量子态。本文首先提出了多体纯量子态的相干本征值，然后在此基础上定义了多体纯态或混合态的相干测度，发现凸屋顶相干测度与基于保真度的几何测度是等价的。这一发现使我们能够给出另一种方法来证明几何测量的一致性是单调的选择性测量的平均。提出了另外两种基于相干本征值的相干测度，并研究了它们的性质。作为应用，利用相干本征值导出了几种著名相干测度的界。特别地，通过提出一个与相干特征值相关的新的相干证据，得到了相干鲁棒性的一个界，并给出了相应的几何解释。
The quantification of coherence is central in quantum information theory and far from being fully understood, particularly for multipartite quantum states. In this work, we first propose the coherence eigenvalue for multipartite pure quantum states and then define the coherence measure for a given multipartite pure or mixed state based on it. It is found that the convex roof coherence measure is equal to the geometric measure based on fidelity. This finding allows us to give an alternative way to prove that the geometric measure of coherence is monotone under selective measurements on average. The other two new coherence measures based on coherence eigenvalue are presented, and their properties are also investigated. As an application, the bounds of several well-known coherence measures are derived by using of coherence eigenvalue. In particular, by proposing a new coherence witness which is related to coherence eigenvalue, we obtain a bound to robustness of coherence and give it a corresponding geometric interpretation.