Geometry of Kirkwood–Dirac classical states: a case study based on discrete Fourier transform
Year: 2024
Type: article
Abstract: The characterization of Kirkwood–Dirac (KD) classicality or non-classicality is very important in quantum information processing. In general, the set of KD classical states with respect to two bases is not a convex polytope (Langreneet al2024J. Math. Phys.65072201), which makes us interested in finding out in which circumstances they do form a polytope. In this paper, we focus on the characterization of KD classicality of mixed states for the case where the transition matrix between two bases is a discrete Fourier transform (DFT) matrix in Hilbert space with dimensionsp2andpq, respectively, where p,q are prime. For the two particular cases we investigate, the sets of extremal points are finite, implying that the set of KD classical states we characterize forms a convex polytope. We show that forp2dimensional system, the set KDA,B+ is a convex hull of the set pure(KDA,B+) based on DFT, where KDA,B+ is the set of KD classical states with respect to two bases and pure(KDA,B+) is the set of all the rank-one projectors of KD classical pure states with respect to two bases. Inpqdimensional system, we believe that this result also holds. Unfortunately, we do not completely prove it, but some meaningful conclusions are obtained about the characterization of KD classicality.
Authors: Ying-Hui Yang, Shuang Yao, Shi-Jiao Geng, Xiao-Li Wang, Pei-Ying Chen
Institution: Henan Polytechnic University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1151905201, G1892128989, G8587254628
OpenAlex ID: W4403013891