Characterizing an Uncertainty Diagram and Kirkwood–Dirac Nonclassicality Based on Discrete Fourier Transform

Autor:	Ying-Hui Yang, Bing-Bing Zhang, Xiao-Li Wang, Shi-Jiao Geng, Pei-Ying Chen
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Kirkwood–Dirac nonclassicality uncertainty diagram discrete Fourier transform complete incompatible bases Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 25, Iss 7, p 1075 (2023)
Druh dokumentu:	article
ISSN:	1099-4300 59738138
DOI:	10.3390/e25071075
Popis:	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.
Databáze:	Directory of Open Access Journals
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