Stationary measure for three-state quantum walk
Stationary measure for three-state quantum walk
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DOI：
10.26421/qic19.11-12-1
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
T. Endo;T. Komatsu;N. Konno;Tomoyuki Terada
中科院分区：
文献类型：
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作者：
T. Endo;T. Komatsu;N. Konno;Tomoyuki Terada
我们主要研究一维三态量子行走。本文从特征值问题出发，给出了一般情况下的平稳测度。首先，我们用新的方法求出传递矩阵，并求解特征值问题。然后得到了具体初态和特征值的平稳测度的一般形式。我们还展示了三态量子阱的定态测度的一些具体例子。未来的一个有趣而关键的问题是弄清楚平稳测度集的全貌。
We focus on the three-state quantum walk (QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly, we get the transfer matrices by our new recipe, and solve the eigenvalue problem. Then we obtain the general form of the stationary measure for concrete initial state and eigenvalue. We also show some specific examples of the stationary measure for the three-state QW. One of the interesting and crucial future problems is to make clear the whole picture of the set of stationary measures.