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One-Dimensional Three-State Quantum Walk with Single-Point Phase Defects

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Abstract

In this paper, we study a three-state quantum walk with a phase defect at a designated position. The coin operator is a parametrization of the eigenvectors of the Grover matrix. We numerically investigate the properties of the proposed model via the position probability distribution, the position standard deviation, and the time-averaged probability at the designated position. It is shown that the localization effect can be governed by the phase defect’s position and strength, coin parameter and initial state.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61202451), the Foundation of Fujian Education Bureau (Grant Nos. JA12062, JA11054), and a Program for Innovative Research Team in Science and Technology in Fujian Province University.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    Yong-Zhen Xu, Gong-De Guo & Song Lin

  2. Key Lab of Network Security and Cryptography, Fujian Normal University, Fuzhou, 350007, China

    Yong-Zhen Xu, Gong-De Guo & Song Lin

Authors
  1. Yong-Zhen Xu
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  2. Gong-De Guo
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  3. Song Lin
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Correspondence to Song Lin.

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Xu, YZ., Guo, GD. & Lin, S. One-Dimensional Three-State Quantum Walk with Single-Point Phase Defects. Int J Theor Phys 55, 4060–4074 (2016). https://doi.org/10.1007/s10773-016-3034-7

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  • DOI: https://doi.org/10.1007/s10773-016-3034-7

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