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We calculated reduced density characteristic matrix (RDCM) for quantum walkon cycles (QWC) to study asymptotic properties of the most general form ofquantum walk on cycles with general $U(2)$ coin operator. As an example,entanglement temperature for general initial state has been calculated andcompared to previous results. Also, we have modified RDCM to derive analyticalexpression for general form of limiting distribution (LD).

Asymptotic Behavior and Limiting Distribution of Quantum Walk on Cycles with General U(2) Coin by Reduced Characteristic Matrix Method