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A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
Caishi Wang1, Suling Ren1, Yuling Tang1
1School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China.
Abstract:
In this paper, we consider limit probability distributions of the quantum walk recently introduced by Wang and Ye (C.S. Wang and X.J. Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Inf. Process. 15 (2016), no. 5, 1897-1908). We first establish several technical theorems, which themselves are also interesting. Then, by using these theorems, we prove that, for a wide range of choices of the initial state, the above-mentioned quantum walk has a limit probability distribution of standard Gauss type, which actually gives a new limit theorem for the walk.
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