Illustration of the quantum central limit theorem by independent addition of spins

1990 ◽  
pp. 349-356 ◽  
Author(s):  
Wilhelm von Waldenfels
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quantum Central Limit Theorem

A q‐analog of the quantum central limit theorem for SUq(2)

1992 ◽  
Vol 33 (8) ◽  
pp. 2768-2778 ◽  
Author(s):  
Romuald Lenczewski ◽  
Krzysztof Podgórski
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quantum Central Limit Theorem

scholarly journals Quantum Walk in Terms of Quantum Bernoulli Noise and Quantum Central Limit Theorem for Quantum Bernoulli Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Caishi Wang ◽  
Ce Wang ◽  
Yuling Tang ◽  
Suling Ren
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Degrees Of Freedom ◽  
Probability Distributions ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Quantum Central Limit Theorem ◽  
Creation Operators ◽  
Internal Degrees Of Freedom

As a unitary quantum walk with infinitely many internal degrees of freedom, the quantum walk in terms of quantum Bernoulli noise (recently introduced by Wang and Ye) shows a rather classical asymptotic behavior, which is quite different from the case of the usual quantum walks with a finite number of internal degrees of freedom. In this paper, we further examine the structure of the walk. By using the Fourier transform on the state space of the walk, we obtain a formula that links the moments of the walk’s probability distributions directly with annihilation and creation operators on Bernoulli functionals. We also prove some other results on the structure of the walk. Finally, as an application of these results, we establish a quantum central limit theorem for the annihilation and creation operators themselves.

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