相干矢量表象中的量子相干性度量

Measuring quantum coherence in coherence-vector representation

摘要:

量子相干性度量最近是量子资源理论中的热点任务. Baumgratz等人已经于2014年提出严格的相干性度量框架.在该框架中，相干性度量的定义要求把量子态固定在希尔伯特空间中一组特定基矢上，其结果是在同一度量下，基矢的变换会引起同一量子态的相干性发生改变.在相干矢量表象中利用相干矢量的旋转性质，一种基于相干矢量归一化模长的相干性度量被提出.在该度量中，同一量子态的相干性独立于基矢的选择.基于该度量的非相干态和非相干算符已经分别定义为经典最大混合态和酉算符.同时,三条重要性质已经得到，分别为非负性、凸性和非相干操作不变性.

Abstract:

Recently, how to measure quantum coherence is a hot topic in the quantum resource theory. In 2014, Baumgratz et al. proposed a rigorous framework to quantify coherence. In this framework, a particular basis of the Hilbert space is required to define the coherence measure, and hence, the proposed coherence measure of the same quantum state does not remain the same under the basis transformations. In this paper, a measure of coherence based on the normalized modulus of the coherent vector is proposed in coherent vector representation, where the property of the coherent vector under basis transformation is considered. The measure of coherence proposed here is independent of the choice of the basis. The incoherent states and incoherent operators based on this measure can also be well defined as the classical maximal mixed states and the unitary operators respectively. And three important properties can be obtained, namely, non-negativity, convexity and invariance on the incoherent operators.