论文标题
由量子Bernoulli声音构建的高维开放量子步行
Higher-Dimensional Open Quantum Walk Constructed from Quantum Bernoulli Noises
论文作者
论文摘要
量子Bernoulli噪声是作用于Bernoulli功能的歼灭和创建操作员，它们在相等的时间内满足规范的反通讯关系（CAR）。在本文中，我们使用Quantum bernoulli噪声在$ d $ d $维整数lattice $ \ mathbb {z}^d $上引入一个开放量子步行的模型，用于一般正整数$ d \ geq 2 $，我们致电$ d $ d $ d $ d $ dimensional-dipermensional open qbn walk。我们获得了$ d $ d $二维开放QBN步行的量子通道表示，并发现它承认``可分离性提供了''属性。我们证明，对于其初始状态的各种选择，$ d $二维的QBN步行步行的限制概率分布为$ d $二维高斯类型。最终，我们在[Ce Wang and Caishi Wang中引入了$ d $维的开放QBN步行和统一量子步行之间的链接，就量子Bernoulli噪声而言，熵2020，22，22，504]。
Quantum Bernoulli noises are annihilation and creation operators acting on Bernoulli functionals, which satisfy the canonical anti-commutation relations (CAR) in equal-time. In this paper, we use quantum Bernoulli noises to introduce a model of open quantum walk on the $d$-dimensional integer lattice $\mathbb{Z}^d$ for a general positive integer $d\geq 2$, which we call the $d$-dimensional open QBN walk. We obtain a quantum channel representation of the $d$-dimensional open QBN walk, and find that it admits the ``separability-preserving'' property. We prove that, for a wide range of choices of its initial state, the $d$-dimensional open QBN walk has a limit probability distribution of $d$-dimensional Gauss type. Finally we unveil links between the $d$-dimensional open QBN walk and the unitary quantum walk recently introduced in [Ce Wang and Caishi Wang, Higher-dimensional quantum walk in terms of quantum Bernoulli noises, Entropy 2020, 22, 504].
