Pretty good state transfer in discrete-time quantum walks. (21st April 2023)

• Record Type: Journal Article
• Authors: Chan, Ada; Zhan, Hanmeng
• Is Part Of: Journal of physics. Volume 56:Number 16(2023)
• Publication Date: 2023-04-21
• Subjects: pretty good state transfer -- discrete-time quantum walk -- coined quantum walk; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/acc4f5
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more specifically, the vertices involved in pretty good state transfer must be strongly cospectral relative to this matrix, and the arccosines of its eigenvalues must satisfy some number theoretic conditions. Using normalized adjacency matrices, cyclic covers, and the theory on linear relations between geodetic angles, we construct several infinite families of walks that exhibits this phenomenon.