混合图上的零转移
Zero transfer on mixed graphs
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中文总结 AI 辅助
本文针对混合图研究量子行走的零转移现象，利用Hermitian邻接矩阵推导其充要条件，并将准则应用于有向循环图，得到不同阶数的相关结果。
中文摘要 AI 辅助
本文研究混合图上的零转移。零转移是一种量子行走现象，即两顶点间的跃迁振幅在所有时刻均恒为零，故二者间不发生任何量子态转移。利用Hermitian邻接矩阵，本文推导了混合图中零转移的充要条件，随后将这些准则应用于有向循环图，得到素数阶的不存在结果、偶数阶的结构限制，以及小阶数的详尽计算分类。
英文摘要
In this paper, we investigate zero transfer on mixed graphs. Zero transfer is a quantum walk phenomenon in which the transition amplitude between two vertices is identically zero for all times, so that no quantum state transfer occurs between them. Using the Hermitian adjacency matrix, we derive necessary and sufficient conditions for zero transfer in mixed graphs. We then specialize these criteria to oriented circulant graphs, obtaining nonexistence results for prime order, structural restrictions for even order, and exhaustive computational classifications for small orders.
