Journal
DISCRETE MATHEMATICS
Volume 343, Issue 11, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.disc.2020.112018
Keywords
Quantum walk; Association scheme; Bose-Mesner algebra; Hamming scheme; Krawtchouk polynomials
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Funding
- National Science and Engineering Research Council (NSERC) of Canada
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Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is relevant in quantum information in particular for entanglement generation in spin networks. We study fractional revival in graphs whose adjacency matrices belong to the Bose-Mesner algebra of association schemes. A specific focus is a characterization of balanced fractional revival (which corresponds to maximal entanglement) in graphs that belong to the Hamming scheme. Our proofs exploit the intimate connections between algebraic combinatorics and orthogonal polynomials. (C) 2020 Published by Elsevier B.V.
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