Abstract
In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897–1908, 2016) as a special case.
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Acknowledgements
The authors are extremely grateful to the referees for their valuable comments and suggestions on improvement of the first version of the present paper. This work is supported by National Natural Science Foundation of China (Grant No. 11461061).
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Wang, C., Wang, C., Ren, S. et al. Open quantum random walk in terms of quantum Bernoulli noise. Quantum Inf Process 17, 46 (2018). https://doi.org/10.1007/s11128-018-1820-2
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DOI: https://doi.org/10.1007/s11128-018-1820-2