Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy the canonical anti-commutation relation (CAR) in equal time. This paper aimed to discuss the classical reduction and ergodicity of quantum exclusion semigroups constructed by QBN. We first study the classical reduction of the quantum semigroups to an Abelian algebra of diagonal elements and the space of off-diagonal elements. We then provide an explicit representation formula by separating the action on off-diagonal and diagonal operators, on which they are reduced to the semigroups of classical Markov chains. Finally, we prove that the asymptotic behavior of the quantum semigroups is equivalent to one of its associated Markov chains, and that the semigroups restricted to the off diagonal space of operators have a zero limit.

量子伯努利噪声（QBN）是作用于伯努利泛函的湮没算子和创造算子族，它同时满足规范的反交换关系（CAR）。本文旨在讨论QBN构造的量子排斥半群的经典约简和遍历性。我们首先研究量子半群到对角元素的阿贝尔代数和非对角元素空间的经典约简。然后，我们通过分离非对角线和对角线算子的作用来提供一个显式的表示公式，在该公式上它们被简化为经典马尔可夫链的半群。最后，我们证明量子半群的渐近行为等价于其相关的马尔可夫链之一，