Let (Ω,ℱ,ℙ) be a probability space and Z=(ZK)k∈ℕ a Bernoulli noise on (Ω,ℱ,ℙ) which has the chaotic representation property. In this paper, we investigate a special family of functionals of Z, which we call the coherent states. First, with the help of Z, we construct a mapping ϕ from l2(ℕ) to ℒ2(Ω,ℱ,ℙ) which is called the coherent mapping. We prove that ϕ has the continuity property and other properties of operation. We then define functionals of the form ϕ(f) with f∈l2 (ℕ) as the coherent states and prove that all the coherent states are total in ℒ2 (Ω,ℱ,ℙ) . We also show that ϕ can be used to factorize ℒ2 (Ω,ℱ,ℙ) . Finally we give an application of the coherent states to calculus of quantum Bernoulli noise.
