论文标题
均匀的开放量子步行在线：现场复发和吸收标准
Homogeneous open quantum walks on the line: criteria for site recurrence and absorption
论文作者
论文摘要
如S. Attal等人所述，在这项工作中，我们研究了开放的量子随机步行。这些对象是用作用于微量级运算符的完全正面地图给出的，这导致了经典，离散时间随机步行的重复问题的最简单量子版本之一。这项工作着重于获得最近邻居的现场复发标准，在整数线上均匀行走，此处介绍的描述利用了开放式步行理论的最新结果，尤其是涉及涉及操作员的降低性属性。这使我们能够在每个站点的内部自由度（硬币空间）的内部自由度为2的情况下获得一个完整的位置复发标准。我们还为内部任意有限的维度和在半融合线上的内部任意有限维度和吸收性问题提供了不可减至的步行的类似结果。
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the recurrence problem for classical, discrete-time random walks. This work focuses on obtaining criteria for site recurrence of nearest-neighbor, homogeneous walks on the integer line, with the description presented here making use of recent results of the theory of open walks, most particularly regarding reducibility properties of the operators involved. This allows us to obtain a complete criterion for site recurrence in the case for which the internal degree of freedom of each site (coin space) is of dimension 2. We also present the analogous result for irreducible walks with an internal degree of arbitrary finite dimension and the absorption problem for walks on the semi-infinite line.
