相互作用Fock空间中的离散时间量子Bernoulli噪声

Discrete Time Quantum Bernoulli Noises in Interacting Fock Spaces

本文提出一种新的离散时间下量子Bernoulli噪声(QBN),并将其引入到相互作用Fock空间中.首先,利用Bernoulli随机变量的量子分解,得到了湮灭、增生、保守算子.然后,构造了相互作用Fock空间中的量子Bernoulli噪声,讨论了它的性质.我们还找到一个算子过程是适应的充要条件.最后,我们重新定义了关于QBN的适应算子过程的积分,并证明了适应算子的鞅性.

We supply a new version of discrete time quantum Bernoulli noises(QBNs),which is taken into interacting Fock spaces.We firstly use the discomposition of Bernoulli random variable to get the annihilation,creation and conservation operators.And then,we construct the quantum Bernoulli noises in interacting Fock spaces,and discuss the properties.We also find the necessary and sufficient condition for an operator process to be adapted.Finally we redefine integrals of adapted operator processes with respect to QBNs and show the martingale property of adapted operators.