Classification of incompatibility for two orthonormal bases

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 $2\le s\le d+1.$ 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.

7 pages, 3 figures

References in corpus (7)

• Quantum theory of successive projective measurements
• Non-disturbing quantum measurements
• Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
• Device-independent quantification of measurement incompatibility
• Quantum Incompatibility of a Physical Context
• Quantum measurement incompatibility in subspaces
• Incompatibility probability of random quantum measurements

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