论文标题
两个正统基础的不相容性的分类
Classification of incompatibility for two orthonormal bases
论文作者
论文摘要
对于两个$ d $二维复合物希尔伯特空间的正直基础，DeBièvre[Phys。莱特牧师。 127，190404（2021）]。在这项工作中，我们介绍了$ s $ order的概念与正整数$ s $满足$ 2 \ leq s \ leq d+1的概念。我们在$ s $ order不兼容，最小支持不确定性和过渡矩阵等级缺陷之间建立了一些关系。例如，我们确定具有任何有限维度的离散傅立叶变换的不兼容顺序。
For two orthonormal bases of a $d$-dimensional complex Hilbert space, the notion of complete incompatibility was introduced recently by De Bièvre [Phys. Rev. Lett. 127, 190404 (2021)]. In this work, we introduce the notion of $s$-order incompatibility with positive integer $s$ satisfying $2\leq s\leq d+1.$ In particular, $(d+1)$-order incompatibility just coincides with the complete incompatibility. We establish some relations between $s$-order incompatibility, minimal support uncertainty and rank deficiency of the transition matrix. As an example, we determine the incompatibility order of the discrete Fourier transform with any finite dimension.
