Discrete-time quantum Bernoulli noises
Discrete-time quantum Bernoulli noises
复制标题
离散时间量子伯努利噪声
DOI：
10.1063/1.3431028
复制
发表时间：
2010-05-01
影响因子：
1.3
通讯作者：
Lu, Yanchun
中科院分区：
文献类型：
--
作者：
Wang, Caishi;Chai, Huifang;Lu, Yanchun
在本文中，我们证明了在离散时间的伯努利泛函空间的湮灭和创造运营商可以很自然地解释为离散时间量子伯努利噪声（QBN）。首先，我们研究他们的代数性质，并证明除其他事项外，家庭的湮灭创造和运营商产生一个交换群的酉运营商。此外，然后通过使用QBN，我们证明了离散时间克拉克公式的一个操作版本。我们还得到了一个基于QBN的必要和充分条件的运营商过程进行调整。定义了适应算子过程关于QBN的积分，并证明了它们的算子鞅性质。最后，我们给出了Bernoulli泛函空间上算子的一个表示公式。
In this paper we show that annihilation and creation operators on the space of Bernoulli functionals in discrete time can be naturally interpreted as discrete-time quantum Bernoulli noises (QBNs). We first examine their algebraic properties and prove among other things that the family of annihilation-creation sum operators generates a commutative group of unitary operators. Additionally, then by using QBN we prove an operator version of the discrete-time Clark formula. We also obtain a QBN-based necessary and sufficient condition for an operator process to be adapted. We define integrals of adapted operator processes with respect to QBN and show their operator martingale property. Finally, we give a representation formula for operators on the space of Bernoulli functionals.