Open quantum walks (OQWs) describe a quantum walker on an underlying graph whose dynamics is purely driven by dissipation and decoherence. Mathematically, they are formulated as completely positive trace preserving (CPTP) maps on the space of density matrices for the walker on the graph. Any microscopically derived OQW must include the possibility of remaining on the same site on the graph when the map is applied. We extend the CPTP map to describe a lazy OQW. We derive a central limit theorem for lazy OQWs on a $d$-dimensional lattice, where the distribution converges to a Gaussian. We show that the properties of this Gaussian computed using conventional methods agree with the general formulas derived from our central limit theorem.

中文翻译：

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惰性开放量子漫步

开放式量子游走（OQW）在基础图上描述了一个量子游走，其动力学完全由耗散和退相干驱动。从数学上讲，它们被构造为图上步行者在密度矩阵空间上的完全正迹线保留（CPTP）映射。应用显微镜时，任何从显微镜得出的OQW都必须包括保留在图形上同一位置的可能性。我们扩展了CPTP映射以描述一个惰性OQW。我们推导了一个中心上的惰性OQW的中心极限定理。$d$维晶格，分布收敛于高斯分布。我们表明，使用常规方法计算出的该高斯性质与从我们的中心极限定理得出的一般公式一致。