2019/10/04 by Chris Godsil, Godsil, Chris, Krystal Guo +3
Engineering · Mathematics · Physics and Astronomy · #05C50 #81P16 #81P68 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Markov Chains and Monte Carlo Methods #Quantum Physics (quant-ph) #graph theory and CDMA systems #math.CO #msc:05C50 #msc:81P16 #msc:81P68 #quant-ph
paper · pdf · doi:10.48550/arxiv.1910.02039
16 pages, 2 figures, 4 tables
arxiv created 2019/10/04 · openalex publication_date 2019/10/04 · arxiv updated 2019/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the diagonal entries of the average mixing matrix of continuous quantum walks. The average mixing matrix is a graph invariant; it is the sum of the Schur squares of spectral idempotents of the Hamiltonian. It is non-negative, doubly stochastic and positive semi-definite. We investigate the diagonal entries of this matrix. We study the graphs for which the trace of the average mixing matrix is maximum or minimum and we classify those which are maximum. We give two constructions of graphs whose average mixing matrices have constant diagonal.