# Limit theorems for the discrete-time quantum walk on a graph with joined half lines

@article{Chisaki2012LimitTF, title={Limit theorems for the discrete-time quantum walk on a graph with joined half lines}, author={Kota Chisaki and Norio Konno and Etsuo Segawa}, journal={Quantum Inf. Comput.}, year={2012}, volume={12}, pages={314-333} }

We consider a discrete-time quantum walk Wt,κ at time t on a graph with joined half lines Jκ, which is composed of κ half lines with the same origin. Our analysis is based on a reduction of the walk on a half line. The idea plays an important role to analyze the walks on some class of graphs with symmetric initial states. In this paper, we introduce a quantum walk with an enlarged basis and show that Wt,κ can be reduced to the walk on a half line even if the initial state is asymmetric. For Wt… CONTINUE READING

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