Fractional revival and association schemes

被引：10

作者：

Chan, Ada ^{[1
]}

Coutinho, Gabriel ^{[2
]}

Tamon, Christino ^{[3
]}

Vinet, Luc ^{[4
]}

Zhan, Hanmeng ^{[4
]}

机构：

[1] York Univ, Dept Math & Stat, Toronto, ON, Canada

[2] Univ Fed Minas Gerais, Dept Comp Sci, Belo Horizonte, MG, Brazil

[3] Clarkson Univ, Dept Comp Sci, Potsdam, NY USA

[4] Univ Montreal, Ctr Rech Math, Montreal, PQ, Canada

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Quantum walk; Association scheme; Bose-Mesner algebra; Hamming scheme; Krawtchouk polynomials;

D O I：

10.1016/j.disc.2020.112018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：15

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