Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
复制标题
DOI：
10.1103/physreva.92.062307
复制
发表时间：
2015-12-03
影响因子：
2.9
通讯作者：
Chandrashekar, C. M.
中科院分区：
文献类型：
--
作者：
Machida, Takuya;Chandrashekar, C. M.
二维离散时间量子行走（DTQW）可以通过在一个空间维度上交替两态DTQW，然后在另一个维度上演化来实现。这被证明是再现一个二维晶格上的四态DTQW的某种配置的概率分布。在这项工作中，我们提出了一个三态交替DTQW与参数化的硬币翻转算子，并表明它可以产生本地化，也观察到的四态DTQW的某些其他配置和不可再生的使用两个状态的交替DTQW。我们将提出三态交替DTQW的两个极限定理。其中一个极限定理描述了返回概率的长时间极限，另一个极限定理给出了步行者在按时间重新标度的空间上的位置的分布收敛。我们发现三态交替DTQW产生的空间纠缠度比四态DTQW产生的空间纠缠度高。使用我们所有的结果，我们概述了这些步行在三个层次的物理系统的相关性。
A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a four-state DTQW on a two-dimensional lattice. In this work we present a three-state alternate DTQW with a parametrized coin-flip operator and show that it can produce localization that is also observed for a certain other configuration of the four-state DTQW and nonreproducible using the two-state alternate DTQW. We will present two limit theorems for the three-state alternate DTQW. One of the limit theorems describes a long-time limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We find that the spatial entanglement generated by the three-state alternate DTQW is higher than that by the four-state DTQW. Using all our results, we outline the relevance of these walks in three-level physical systems.