Chinese Journal of Quantum Electronics, Volume. 42, Issue 2, 217(2025)

One⁃dimensional topological coinless quantum walks in optical waveguides

MENG Ya*
Author Affiliations
  • Department of Physics, Xinzhou Normal University, Xinzhou 034000, China
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    References(29)

    [1] Aharonov Y, Davidovich L, Zagury N. Quantum random walks[J]. Physical Review A, 48, 1687-1690(1993).

    [2] Farhi E, Gutmann S. Quantum computation and decision trees[J]. Physical Review A, 58, 915-928(1998).

    [3] Zhang R, Yang P. Recurrence of unbiased quantum walk[J]. Chinese Journal of Quantum Electronics, 35, 697-704(2018).

    [4] Zhang R, Ling K. Research on entanglement between coin and walker in quantum walk[J]. Chinese Journal of Quantum Electronics, 39, 446-451(2022).

    [5] Patel A, Raghunathan K S, Rungta P. Quantum random walks do not need a coin toss[J]. Physical Review A, 71, 032347(2005).

    [6] Kitagawa T, Rudner M S, Berg E et al. Exploring topological phases with quantum walks[J]. Physical Review A, 82, 033429(2010).

    [7] Kitagawa T, Broome M A, Fedrizzi A et al. Observation of topologically protected bound states in photonic quantum walks[J]. Nature Communications, 3, 882(2012).

    [8] Asbóth J K. Symmetries, topological phases, and bound states in the one-dimensional quantum walk[J]. Physical Review B, 86, 195414(2012).

    [9] Asbóth J K, Obuse H. Bulk-boundary correspondence for chiral symmetric quantum walks[J]. Physical Review B, 88, 121406(2013).

    [10] Cardano F, Maffei M, Massa F et al. Statistical moments of quantum-walk dynamics reveal topological quantum transitions[J]. Nature Communications, 7, 11439(2016).

    [11] Cardano F, D'Errico A, Dauphin A et al. Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons[J]. Nature Communications, 8, 15516(2017).

    [12] Ramasesh V V, Flurin E, Rudner M et al. Direct probe of topological invariants using Bloch oscillating quantum walks[J]. Physical Review Letters, 118, 130501(2017).

    [13] Wang B, Chen T, Zhang X D. Experimental observation of topologically protected bound states with vanishing Chern numbers in a two-dimensional quantum walk[J]. Physical Review Letters, 121, 100501(2018).

    [14] Chen C, Ding X, Qin J et al. Observation of topologically protected edge states in a photonic two-dimensional quantum walk[J]. Physical Review Letters, 121, 100502(2018).

    [15] Xu X Y, Wang Q Q, Pan W W et al. Measuring the winding number in a large-scale chiral quantum walk[J]. Physical Review Letters, 120, 260501(2018).

    [16] Xu X Y, Wang Q Q, Tao S J et al. Experimental classification of quenched quantum walks by dynamical Chern number[J]. Physical Review Research, 1, 033039(2019).

    [17] Xu X Y, Wang Q Q, Heyl M et al. Measuring a dynamical topological order parameter in quantum walks[J]. Light, 9, 7(2020).

    [18] Wang Q Q, Xu X Y, Pan W W et al. Robustness of entanglement as an indicator of topological phases in quantum walks[J]. Optica, 7, 53-58(2020).

    [19] Xiao L, Zhan X, Bian Z H et al. Observation of topological edge states in parity⁃time⁃symmetric quantum walks[J]. Nature Physics, 13, 1117-1123(2017).

    [20] Xiao L, Deng T S, Wang K K et al. Non-Hermitian bulk⁃boundary correspondence in quantum dynamics[J]. Nature Physics, 16, 761-766(2020).

    [21] Lin Q, Li T Y, Xiao L et al. Topological phase transitions and mobility edges in non-Hermitian quasicrystals[J]. Physical Review Letters, 129, 113601(2022).

    [22] Tang H, Lin X F, Feng Z et al. Experimental two-dimensional quantum walk on a photonic chip[J]. Science Advances(2018).

    [23] Tang H, Banchi L, Wang T Y et al. Generating Haar-uniform randomness using stochastic quantum walks on a photonic chip[J]. Physical Review Letters, 128, 050503(2022).

    [24] Jiao Z Q, Longhi S, Wang X W et al. Experimentally detecting quantized Zak phases without chiral symmetry in photonic lattices[J]. Physical Review Letters, 127, 147401(2021).

    [25] Maczewsky L J, Zeuner J M, Nolte S et al. Observation of photonic anomalous Floquet topological insulators[J]. Nature Communications, 8, 13756(2017).

    [26] Meng Y, Chen G, Jia S T. Second-order topological insulator in a coinless discrete-time quantum walk[J]. Physical Review A, 102, 012203(2020).

    [27] Meng Y. Topological corner states in non-unitary coinless discrete-time quantum walks[J]. Frontiers in Physics, 10, 861125(2022).

    [28] Hasan M Z, Kane C L. Colloquium: Topological insulators[J]. Reviews of Modern Physics, 82, 3045-3067(2010).

    [29] Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 83, 1057-1110(2011).

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    Ya MENG. One⁃dimensional topological coinless quantum walks in optical waveguides[J]. Chinese Journal of Quantum Electronics, 2025, 42(2): 217

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    Paper Information

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    Received: Jul. 3, 2023

    Accepted: --

    Published Online: Apr. 1, 2025

    The Author Email: Ya MENG (mengya418@163.com)

    DOI:10.3969/j.issn.1007-5461.2025.02.007

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