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Abstract We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions, generalized classical random walk with memory can degrade into classical random walk and classical random walk with memory. Based on its various spreading speed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring the quantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walks with memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walk and classical random walk with memory by coherence non-generating channels. Also, we find that for another class of coherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of the coin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore the relationship between coherence and quantum walk.
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Received: 13 October 2020
Revised: 19 November 2020
Accepted manuscript online: 30 December 2020
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PACS:
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03.67.-a
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(Quantum information)
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02.50.-r
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(Probability theory, stochastic processes, and statistics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11774205) and the Young Scholars Program of Shandong University. |
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Corresponding Authors:
†Corresponding author. E-mail: xyhu@sdu.edu.cn
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Cite this article:
Zishi Chen(陈子石) and Xueyuan Hu(胡雪元) Quantum walk under coherence non-generating channels 2021 Chin. Phys. B 30 030305
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