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Keywords = Kirkwood–Dirac nonclassicality

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13 pages, 367 KiB  
Article
Characterizing an Uncertainty Diagram and Kirkwood–Dirac Nonclassicality Based on Discrete Fourier Transform
by Ying-Hui Yang, Bing-Bing Zhang, Xiao-Li Wang, Shi-Jiao Geng and Pei-Ying Chen
Entropy 2023, 25(7), 1075; https://doi.org/10.3390/e25071075 - 17 Jul 2023
Cited by 2 | Viewed by 1392
Abstract
In this paper, we investigate an uncertainty diagram and Kirkwood–Dirac (KD) nonclassicality based on discrete Fourier transform (DFT) in a d-dimensional system. We first consider the uncertainty diagram of the DFT matrix, which is a transition matrix from basis A to basis [...] Read more.
In this paper, we investigate an uncertainty diagram and Kirkwood–Dirac (KD) nonclassicality based on discrete Fourier transform (DFT) in a d-dimensional system. We first consider the uncertainty diagram of the DFT matrix, which is a transition matrix from basis A to basis B. Here, the bases A, B are not necessarily completely incompatible. We show that for the uncertainty diagram of the DFT matrix, there is no “hole” in the region of the (nA,nB) plane above and on the line nA+nB=d+1. Then, we present where the holes are in the region strictly below the line and above the hyperbola nAnB=d. Finally, we provide an alternative proof of the conjecture about KD nonclassicality based on DFT. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Information Processing)
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