we investigate several central limit theorems for a discrete-time three-state quantum walks on the real line. We introduce a set of special coin update operators—the rotation matrix, whose degrees of freedom include rotation axis and angle. We obtain their explicit forms of the limit distribution for specific axes and angles and we also derive their simulating distribution curves through computer for unsolvable general unitary matrices. The results reveal that three state quantum walks exhibit three interesting phenomena that differ from wo-state quantum walks.   

This work is jointed with Hao Jiang and Chengzhi Xing.

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