Discrete-time quantum Bernoulli noises

作者：Wang Caishi^*; Chai Huifang; Lu Yanchun

来源：Journal of Mathematical Physics, 2010, 51(5): 053528.

DOI：10.1063/1.3431028

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.

• 出版日期2010-5
• 单位西北师范大学