A Class Of Quantum Random Walks In The Environment Of Quantum Bernoulli Noises

As a quantum analogue of classical random walk,quantum random walk belongs to the research category of quantum probability theory,and it has been widely used in quantum information,quantum computation and other fields.Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals,which satisfy a anti-commutation relation(CAR)in equal-time,so it is suitable to describe the environmental effects of quantum systems.In this paper,we discussed the application of quantum Bernoulli noises in quantum random walk The main works are as followsFirstly,we introduced a new model of quantum random walk using quantum Bernoulli noises,it is proved that the time evolution equation of quantum random walk has unitary property,we got the unitary representation of the quantum random walk in l2(Z,H),and which unitary operator is self-adjointSecondly,using the canonical isomorphism,we derived the unitary representa-tion of the introduced quantum random walk in tensor space l2(X)(?)H,and also obtained the construction of the corresponding unitary operator.Furthermore,we discussed the structural properties of the introduced quantum random walk using Fourier transformThirdly,we investigated the dynamic properties of the introduced quantum random walk.By mathematical induction,we given the probability distribution of the quantum random walk in specific initial state,and it is proved that the new model has strong local properties.