# Realization of the probability laws in the quantum central limit theorems by a quantum walk

@article{Machida2013RealizationOT, title={Realization of the probability laws in the quantum central limit theorems by a quantum walk}, author={T. Machida}, journal={Quantum Inf. Comput.}, year={2013}, volume={13}, pages={430-438} }

Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there are four notions of independence (free, monotone, commuting, and boolean independence) and quantum central limit theorems associated to each independence have been investigated. The relation between quantum walks and quantum probability theory is still…

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