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Fractional Revival and Association Schemes | | Ada Chan
; Gabriel Coutinho
; Christino Tamon
; Luc Vinet
; Hanmeng Zhan
; | | Date: |
10 Jul 2019 | | Abstract: | 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. | | Source: | arXiv, 1907.4729 | | Services: | Forum | Review | PDF | Favorites | |
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