两类阿贝尔Cayley图上的完全状态转移

Perfect state transfer of two classes of abelian Cayley graphs

完全状态转移在量子信息传输以及量子计算中有重要的应用,本文利用有限阶阿贝尔群上的特征、等价类,有理数域上的p-adic赋值等理论,通过计算得出两类有限阶阿贝尔群G=Z_4?Z_8,G=Z_8?Z_8上的Cayley图有完全状态转移。

The perfect state transfer(PST)is of great significance for its applications in quantum information transmission and quantum computation.In this paper,based on the theory of character and equivalent classes of the finite abelian group and that of the p-adic valuation on rational number filed,we obtain the fact that two classes of finite abelian groups G=Z4+Z8 and G=Z8+Z8 have the PST of Cayley graphs.