Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

中文翻译：

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量子伯努利噪声环境中的高维开放量子行走

开放量子游走（OQW）（也称为开放量子随机游走）是概率论中经典马尔可夫链的量子类似物，在量子信息和量子计算中具有潜在应用。量子伯努利噪声 (QBN) 是作用于伯努利泛函的湮灭和创造算子，可用作开放量子系统的环境。在本文中，通过使用 QBN 作为环境，我们在一般的高维整数格上引入了 OQW。我们获得了行走的量子通道表示，这表明行走确实是一个 OQW。我们证明了行走的所有状态都是可分离的，前提是它的初始状态是可分离的。我们还证明，对于某些初始状态，游走具有高维高斯类型的极限概率分布。最后，