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.

中文翻译：

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部分复兴和联合计划

如果连续时间量子游走将一个顶点的特征向量统一映射到两个顶点的特征向量的叠加，则图中的两个顶点之间会发生分数恢复。这种现象与量子信息有关，特别是与自旋网络中的纠缠生成有关。我们研究了邻接矩阵属于关联方案的 Bose-Mesner 代数的图中的分数复兴。一个特定的焦点是属于汉明方案的图中的平衡分数复兴（对应于最大纠缠）的特征。我们的证明利用了代数组合和正交多项式之间的密切联系。