中文摘要：

量子相干性是量子信息处理的基本要素，在量子计算中扮演着重要的角色．为了便于讨论量子相干性在量子计算中的作用，本文从离散Wigner函数角度对量子相干性进行了探讨．首先对奇素数维量子系统的离散Wigner函数进行了分析，分离出表征相干性的部分，提出了一种可能的基于离散Wigner函数的量子相干性度量方法，并对其进行了量子相干性度量规范的分析；同时也比较了该度量与f1范数相干性度量之间的关系．重要的是，这种度量方法能够明确给出量子相干性程度与衡量量子态量子计算加速能力的负性和之间不等式关系，由此可以解析地解释量子相干性仅是量子计算加速的必要条件．

英文摘要：

Quantum coherence is an essential ingredient in quantum information processing and plays an important role in quantum computation. Therefore, it is a hot issue about how to quantify the coherence of quantum states in theoretical framework. The coherence effect of a state is usually described by the off-diagonal elements of its density matrix with respect to a particular reference basis. Recently, based on the established notions from quantitative theory of entanglement, a resource theory of coherence quantification has been proposed. In the theory framework, a proper measure of coherence should satisfy three criteria： the coherence should be zero for all incoherent state; the coherence should not increase under mixing quantum states; the coherence should not increase under incoherent operations. Then, a number of coherence measures have been suggested, such as ll norm of coherence and the relative entropy of coherence Wigner function is known as an important tool to study the non-classical property of quantum states for continuous- variable quantum systems. It has been generalized to finite-dimensional Hilbert spaces, and named as discrete Wigner function. The magic property of quantum states, which promotes stabilizer computation to universal quantum computation, can be generally measured by the absolute sum of the negative items （negativity sum） in the discrete Wigner function of the observed quantum states. In this paper we investigate quantum coherence from the view of discrete Wigner function. From the definition of the discrete Wigner function of the quantum systems with odd prime dimensions, for a given density matrix we analyze in phase space the performance of its diagonal and off-diagonal items. We find that, the discrete Wigner function of a quantum state contains two aspects： the true quantum coherence and the classical mixture, where the part of classical mixture can be excluded by only considering the discrete Wigner function of the diagonal items of the density matrix. Thus, we propose a