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arXiv · 2203.06460

Classification of incompatibility for two orthonormal bases

Jianwei Xu
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Abstract

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.

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Jianwei Xu. 2022-08-27. Classification of incompatibility for two orthonormal bases. https://doi.org/10.1103/physreva.106.022217

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