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Quantum Information Processing

, 17:215 | Cite as

Weak limit theorem for a nonlinear quantum walk

  • Masaya Maeda
  • Hironobu Sasaki
  • Etsuo Segawa
  • Akito SuzukiEmail author
  • Kanako Suzuki
Article

Abstract

This paper continues the study of large time behavior of a nonlinear quantum walk begun in Maeda et al. (Discrete Contin Dyn Syst 38:3687–3703, 2018). In this paper, we provide a weak limit theorem for the distribution of the nonlinear quantum walk. The proof is based on the scattering theory of the nonlinear quantum walk, and the limit distribution is obtained in terms of its asymptotic state.

Keywords

Quantum walk Nonlinear quantum walk Scattering theory Weak limit theorem 

Notes

Acknowledgements

M.M. was supported by the JSPS KAKENHI Grant Numbers JP15K17568, JP17H02851, and JP17H02853. H.S. was supported by JSPS KAKENHI Grant Number JP17K05311. E.S. acknowledges the financial support from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) Japan Society for the Promotion of Science (Grant No. 16K17637 and No. 16K03939). A.S. was supported by JSPS KAKENHI Grant Numbers JP26800054 and JP18K03327. K.S acknowledges JSPS Grant-in-Aid for Scientific Research (C) 26400156 and 18K03354.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Informatics, Faculty of ScienceChiba UniversityChibaJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.Division of Mathematics and Physics, Faculty of EngineeringShinshu UniversityNaganoJapan
  4. 4.College of ScienceIbaraki UniversityMitoJapan

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