2024/04/25 by Sooyeong Kim, Hermie Monterde, Kim, Sooyeong +9 · 3 citations
Computer Science · #05C50 #05C76 #15A18 #81P45 #81Q10 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2404.16654
openalex publication_date 2024/04/25 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28
An s-pair state in a graph is a quantum state of the form eu+sev, where u and v are vertices in the graph and s is a non-zero complex number. If s=-1 (resp., s=1), then such a state is called a pair state (resp. plus state). In this paper, we develop the theory of perfect s-pair state transfer in continuous quantum walks, where the Hamiltonian is taken to be the adjacency, Laplacian or signless Laplacian matrix of the graph. We characterize perfect s-pair state transfer in complete graphs, cycles and antipodal distance-regular graphs admitting vertex perfect state transfer. We construct infinite families of graphs with perfect s-pair state transfer using quotient graphs and graphs that admit fractional revival. We provide necessary and sufficient conditions such that perfect state transfer between vertices in the line graph relative to the adjacency matrix is equivalent to perfect state transfer between the plus states formed by corresponding edges in the graph relative to the signless Laplacian matrix. Finally, we characterize perfect state transfer between vertices in the line graphs of Cartesian products relative to the adjacency matrix.