论文标题
开放量子随机步行到量子步行之间的跨界
A crossover between open quantum random walks to quantum walks
论文作者
论文摘要
我们提出了一个中间步行，连续连接开放的量子随机步行和一个量子步行，并带有参数$ m \ in \ mathbb {n} $控制反校正效果；如果$ m = 1 $，则步行与开放的量子随机步行一致，而$ M = \ infty $，步行与量子步行一致。我们定义了一种措施，该度量恢复了$ \ mathbb {z} $ for $ m = \ infty $和$ m = 1 $的常规概率度量，我们通过数值模拟观察中间行为，以了解各种正值$ m $。在$ m = 2 $的情况下，我们在分析上表明，即使在开放的量子随机步行中，量子步行的典型行为也出现了。更确切地说，我们同时观察到弹道向左和右侧的弹道移动，以及该助行器的本地化。该分析基于Kato的线性操作员的扰动理论。我们更详细地分析了该限制定理，并表明上述三种模式由高斯分布描述。
We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters $M\in \mathbb{N}$ controlling a decoherence effect; if $M=1$, the walk coincides with an open quantum random walk, while $M=\infty$, the walk coincides with a quantum walk. We define a measure which recovers usual probability measures on $\mathbb{Z}$ for $M=\infty$ and $M=1$ and we observe intermediate behavior through numerical simulations for varied positive values $M$. In the case for $M=2$, we analytically show that a typical behavior of quantum walks appears even in a small gap of the parameter from the open quantum random walk. More precisely, we observe both the ballistically moving towards left and right sides and localization of this walker simultaneously. The analysis is based on Kato's perturbation theory for linear operator. We futher analyze this limit theorem in more detail and show that the above three modes are described by Gaussian distributions.
