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arXiv · 1710.01482

Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension

Kei Saito
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Abstract

The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The probability distribution of a class of QQWs is the same as that of the QW. On the other hand, a numerical simulation suggests that the probability distribution of a QQW is different from the QW. In this paper, we clarify the difference between the QQW and the QW by weak limit theorems for a class of QQWs.

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Kei Saito. 2017-10-04. Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension. https://arxiv.org/abs/1710.01482

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