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• W4384694693 abstract "In this paper, we investigate the Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform (DFT) in a $d$ dimensional system. The uncertainty diagram of complete incompatibility bases $mathcal {A},mathcal {B}$ are characterized by De Bi`{e}vre [arXiv: 2207.07451]. We show that for the uncertainty diagram of the DFT matrix which is a transition matrix from basis $mathcal {A}$ to basis $mathcal {B}$, there is no ``hole in the region of the $(n_{mathcal {A}}, n_{mathcal {B}})$-plane above and on the line $n_{mathcal {A}}+n_{mathcal {B}}geq d+1$, whether the bases $mathcal {A},mathcal {B}$ are not complete incompatible bases or not. Then we present that the KD nonclassicality of a state based on the DFT matrix can be completely characterized by using the support uncertainty relation $n_{mathcal {A}}(psi)n_{mathcal {B}}(psi)geq d$, where $n_{mathcal {A}}(psi)$ and $n_{mathcal {B}}(psi)$ count the number of nonvanishing coefficients in the basis $mathcal {A}$ and $mathcal {B}$ representations, respectively. That is, a state $|psirangle$ is KD nonclassical if and only if $n_{mathcal {A}}(psi)n_{mathcal {B}}(psi)> d$, whenever $d$ is prime or not. That gives a positive answer to the conjecture in [Phys. Rev. Lett. textbf{127}, 190404 (2021)]." @default.
• W4384694693 created "2023-07-20" @default.
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• W4384694693 date "2023-07-17" @default.
• W4384694693 modified "2023-09-25" @default.
• W4384694693 title "Characterizing an Uncertainty Diagram and Kirkwood–Dirac Nonclassicality Based on Discrete Fourier Transform" @default.
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• W4384694693 doi "https://doi.org/10.3390/e25071075" @default.
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