Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
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DOI：
10.1007/s11128-011-0353-8
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发表时间：
2013-01-01
影响因子：
2.5
通讯作者：
Segawa, Etsuo
中科院分区：
文献类型：
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作者：
Konno, Norio;Luczak, Tomasz;Segawa, Etsuo
本文讨论了Konno(Quantum inf Proc 9：405,2010)提出的具有原点空间微扰的量子行走(QW)的三种度量：时间平均极限度量、弱极限度量和平稳度量。从前两个测量中，我们看到步态中的弹道行为和局部化行为共存，这是一个连续的结果(Konno in Quantum Inf Proc 9：405,2010；Quantum Inf Proc 8：387-399,2009)。对于弱极限测度，我们提出了一类普适性的QWS。结果表明，具有弹道扩散的典型空间均匀量子水波属于普适性类。我们发现，这里处理的步态有一个缺陷，也属于这个班级。我们主要考虑从原点开始的步行。然而，当我们去掉这一限制时，我们得到了行走的一个静止的度量。因此，通过选择平稳测度中的参数，我们分别得到了作为Hadamard行走的平稳测度和具有一个缺陷的行走的时间平均极限测度的一致测度。
We treat three types of measures of the quantum walk (QW) with the spatial perturbation at the origin, which was introduced by Konno (Quantum Inf Proc 9:405, 2010): time averaged limit measure, weak limit measure, and stationary measure. From the first two measures, we see a coexistence of the ballistic and localized behaviors in the walk as a sequential result following (Konno in Quantum Inf Proc 9:405, 2010; Quantum Inf Proc 8:387-399, 2009). We propose a universality class of QWs with respect to weak limit measure. It is shown that typical spatial homogeneous QWs with ballistic spreading belong to the universality class. We find that the walk treated here with one defect also belongs to the class. We mainly consider the walk starting from the origin. However when we remove this restriction, we obtain a stationary measure of the walk. As a consequence, by choosing parameters in the stationary measure, we get the uniform measure as a stationary measure of the Hadamard walk and a time averaged limit measure of the walk with one defect respectively.