Partial coherence with application to the monotonicity problem of coherence involving skew information
Partial coherence with application to the monotonicity problem of coherence involving skew information
复制标题
部分一致性及其在涉及倾斜信息的一致性单调性问题中的应用
DOI：
10.1103/physreva.96.022136
复制
发表时间：
2017-08-28
影响因子：
2.9
通讯作者：
Sun, Yuan
中科院分区：
文献类型：
--
作者：
Luo, Shunlong;Sun, Yuan
在量子力学中，一个状态相对于量子测量的量子相干性可以用测量必须摧毁的量子性来确定。特别是，二分体态相对于局域量子测量的量子相干性编码了态中的量子关联。如果对局域测量采取最小化，那么从相干性的角度来看，就会得到捕捉量子关联的量词。在这种情况下，量子不协调可以被识别为最小相干，而相干是通过相干的相对熵来衡量的。量子不协调量化了必须被量子测量破坏的最小关联。为了在一般的背景下倡导和阐述这一思想，我们首先回顾了相对于Lüders测量的相干性，它相对于冯·诺依曼测量(或等价地，正交基)扩展了相干性的概念，并通过两个典型例子强调了量子不协调作为最小相干性产生的观察结果。然后，我们从相干的角度介绍了一些新的量子关联测量方法，并通过实例加以说明，研究了它们的基本性质和含义，并指出了它们在量子计量学中的应用。版权所有c©Epla，2017年简介。-量子相干产生于叠加原理，是量子力学的核心，自量子理论诞生以来，一直在量子力学中发挥着核心作用。干涉是量子相干最显著的特征。近年来，连贯的表征和量化引起了极大的兴趣[1-10]。与此同时，随着量子信息论的出现，量子关联，包括纠缠和量子不协调，作为叠加的表现形式得到了广泛的研究[11-31]。由于量子相干和量子关联的同源(即叠加)，研究它们之间的关系和相互作用具有重要的理论意义。众所周知，一方面，相干(叠加)是量子力学的一个独特特征，在许多量子任务中起着至关重要的作用，例如干涉测量和量子算法，包括Grover搜索和Shor因式分解[32，33]，另一方面，量子关联已经被认为是量子信息处理中的有用资源，包括量子测量，如相位估计[34-40]。特别是，Girolami等人。根据量子费舍尔信息得出的不协调来量化量子态的干涉功率[39]。Giorda和Allegra发现了参数估计中的量子Fisher信息和关于最佳测量的相干性的二次变化之间的关系[40]。Ma等人。定量地研究了从相干到量子不协调的转换[30]。所有这些研究表明，量子相干和量子关联之间的相互作用，以及它们对量子任务的影响，在量子信息论中具有基本的意义，揭示量子相干和量子关联之间的深层联系是可取的。在这项工作中，我们将展示如何通过优化从相干度量自然产生量子关联度量。我们将通过几个例子来说明这一思想，揭示与现有的一些量子不协调度量的关系，并介绍一些新的量子关联度量。工作安排如下。我们首先回顾相对于Lüders度量的一致性，作为相对于von Neumann度量(正交基)的一致性的扩展。这对于从相干的角度处理两部分或多部分系统中的量子关联是必要的。然后我们举例说明了这两个
In quantum mechanics, quantum coherence of a state relative to a quantum measurement can be identified with the quantumness that has to be destroyed by the measurement. In particular, quantum coherence of a bipartite state relative to a local quantum measurement encodes quantum correlations in the state. If one takes minimization with respect to the local measurements, then one is led to quantifiers which capture quantum correlations from the perspective of coherence. In this vein, quantum discord, which quantifies the minimal correlations that have to be destroyed by quantum measurements, can be identified as the minimal coherence, with the coherence measured by the relative entropy of coherence. To advocate and formulate this idea in a general context, we first review coherence relative to Lüders measurements which extends the notion of coherence relative to von Neumann measurements (or equivalently, orthonomal bases), and highlight the observation that quantum discord arises as minimal coherence through two prototypical examples. Then, we introduce some novel measures of quantum correlations in terms of coherence, illustrate them through examples, investigate their fundamental properties and implications, and indicate their applications to quantum metrology. Copyright c © EPLA, 2017 Introduction. – Quantum coherence, which arises from the superposition principle and lies at the heart of quantumness, has played a central role in quantum mechanics ever since the birth of quantum theory. Interference is the most prominent feature of quantum coherence. In recent years, characterization and quantification of coherence have attracted great interest [1–10]. In the meantime, with the emergence of quantum information theory, quantum correlations, including entanglement and quantum discord, have been extensively studied as manifestations of superposition [11–31]. Because of the same origin (i.e., superposition) of quantum coherence and quantum correlations, it is of theoretical interest to study the relationship and interplay between them. It is well established that, on the one hand, coherence (superposition) is a unique feature of quantum mechanics and plays a crucial role in many quantum tasks such as interferometry and quantum algorithms including Grover’s search and Shor’s factorization [32,33], and on the other hand, quantum correlations have been identified as useful resource in quantum information processing including quantum metrology such as phase estimation [34–40]. In particular, Girolami et al. quantified the interferometric power of quantum states in terms of discord derived from quantum Fisher information [39]. Giorda and Allegra found a relation between quantum Fisher information in parameter estimation and the second variation of coherence with respect to the optimal measurement [40]. Ma et al. studied the conversion from coherence to quantum discord in a quantitative way [30]. All these investigations show that the interplay between quantum coherence and quantum correlations, as well as their implications for quantum tasks, are of basic significance in quantum information theory, and it is desirable to unravel deep connections between quantum coherence and quantum correlations. In this work, we will show how measures of quantum correlations arise naturally from coherence measures via optimization. We will illustrate the idea via several examples, reveal relations with some existent measures of quantum discord, and also introduce some novel measures of quantum correlations. The work is arranged as follows. We first review coherence relative to Lüders measurements, as an extension of coherence relative to von Neumann measurements (orthonormal bases). This is necessary for treating quantum correlations in bipartite or multipartite systems from the perspective of coherence. We then illustrate that two