Pretty good state transfer in discrete-time quantum walks
Pretty good state transfer in discrete-time quantum walks
复制标题
离散时间量子行走中相当好的状态转移
DOI：
10.1088/1751-8121/acc4f5
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Hanmeng Zhan
中科院分区：
文献类型：
--
作者：
Ada Chan;Hanmeng Zhan
我们建立了离散时间量子行走中较好的态转移理论。对于一类游动，我们证明了相当好的状态转移是由图的某些Hermite邻接矩阵的谱所表征的，更具体地说，相当好的状态转移所涉及的顶点必须是相对于这个矩阵的强共谱，并且其特征值的反余弦必须满足一些数论条件.利用正规邻接矩阵、循环覆盖和测地角之间的线性关系理论，我们构造了几个表现这种现象的无限族。
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more specifically, the vertices involved in pretty good state transfer must be strongly cospectral relative to this matrix, and the arccosines of its eigenvalues must satisfy some number theoretic conditions. Using normalized adjacency matrices, cyclic covers, and the theory on linear relations between geodetic angles, we construct several infinite families of walks that exhibits this phenomenon.