# One-dimensional quantum walks via generating function and the CGMV method

@article{Konno2014OnedimensionalQW, title={One-dimensional quantum walks via generating function and the CGMV method}, author={Norio Konno and Etsuo Segawa}, journal={Quantum Inf. Comput.}, year={2014}, volume={14}, pages={1165-1186} }

We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law" decay around the origin and a "strongly" ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with linear scaling whose density has two delta measures at $x=0$ (the origin) and $x=1$ (the bottom) without… CONTINUE READING

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