A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises

Entropy

Caishi Wang¹  Suling Ren¹  Yuling Tang¹ 

[1] School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;

关键词: quantum walk;    quantum Bernoulli noises;    limit theorem;   

DOI  :  10.3390/e22040486

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown