论文标题
在阿贝里亚人群上的双层杂货图上的完美状态转移
Perfect state transfer on bi-Cayley graphs over abelian groups
论文作者
论文摘要
在过去的十年中，对图表上完美的状态转移的研究引起了很多关注，因为它在量子信息处理和量子计算中的应用。理想的状态转移被认为是一种罕见的现象。本文为在任何给定的有限阿贝尔组中具有完美状态转移的双层杂货图建立了必要和充分的条件。作为推论，在与阿贝尔组，（广义的）二面基团，半二面群和广义的季季基团的Cayley图上获得了许多已知和新的结果。尤其是，我们举例说明了一个连接的非正态分式cayley图，而在两个不同的顶点之间具有完美状态转移的二面体群体，这是不可能的。
The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation. Perfect state transfer is understood to be a rare phenomenon. This paper establishes necessary and sufficient conditions for a bi-Cayley graph having perfect state transfer over any given finite abelian group. As corollaries, many known and new results are obtained on Cayley graphs having perfect state transfer over abelian groups, (generalized) dihedral groups, semi-dihedral groups and generalized quaternion groups. Especially, we give an example of a connected non-normal Cayley graph over a dihedral group having perfect state transfer between two distinct vertices, which was thought impossible.
