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A weak limit theorem for a class of long-range-type quantum walks in 1d

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Abstract

We derive the weak limit theorem for a class of long-range-type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave operators exist and are complete.

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Acknowledgements

The author would like to thank A. Suzuki for various comments and constant encouragements. The author would also like to thank H. Ohno and S. Richard for helpful comments. This work was supported by the Research Institute of Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.

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  1. National Institute of Technology, Hachinohe College, Hachinohe, 039-1192, Japan

    Kazuyuki Wada

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Wada, K. A weak limit theorem for a class of long-range-type quantum walks in 1d. Quantum Inf Process 19, 2 (2020). https://doi.org/10.1007/s11128-019-2491-3

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