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Coherence of one-dimensional quantum walk on cycles

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Abstract

Quantum coherence plays a central role in quantum mechanics and provides essential power for quantum information processing. In this paper, we study the dynamics of the \(l_1\) norm coherence in one-dimensional quantum walk on cycles for two initial states. For the first initial state, the walker starts from a single position. The coherence increases with the number of steps at the beginning and then fluctuates over time after approaching to saturation. The coherence with odd number of sites is much larger than that with even number of sites. Another initial state, i.e., the equally superposition state, is also considered. The coherence of the whole system is proved to be \(N-1\) (\(2N-1\)) for any odd (even) time step where N is the number of sites. We also investigate the influence of two unitary noises, i.e., noisy Hadamard operator and broken link, on the coherence evolution.

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Notes

  1. By curve fitting, we have \(C(|{\varPsi }(t)\rangle )=1.527 t^{0.9405}\) and \(C(Tr_C(|{\varPsi }(t)\rangle ))=0.5818 t^{0.9626}\).

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61502179, 61472452, 11647140, 61772565), the Natural Science Foundation of Guangdong Province of China (Nos. 2014A030310265, 2014A030313157, 2017A030313378), the Science and Technology Program of Guangzhou City of China (No. 201707010194), the Fundamental Research Funds for the Central Universities (No. 17lgzd29), the Research Foundation for Talented Scholars of Foshan University (No. gg040996), the Science Foundation for Young Teachers of Wuyi University (No. 2015zk01) and the Doctoral Research Foundation of Wuyi University (No. 2017BS07). H.Z. Situ is sponsored by the State Scholarship Fund of the China Scholarship Council.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Foshan University, Foshan, 528000, China

    Zhimin He

  2. School of Economics and Management, Wuyi University, Jiangmen, 529020, China

    Zhiming Huang

  3. School of Data and Computer Science, Sun Yat-Sen University, Guangzhou, 510006, China

    Lvzhou Li

  4. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Haozhen Situ

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  1. Zhimin He
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Correspondence to Haozhen Situ.

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He, Z., Huang, Z., Li, L. et al. Coherence of one-dimensional quantum walk on cycles. Quantum Inf Process 16, 271 (2017). https://doi.org/10.1007/s11128-017-1724-6

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