Effects of initial states on continuous-time quantum walk in the optical waveguide array

Continuous-time quantum random walk is constructed when photons propagate passing the branches of the waveguide array. It is possible to make quantum simulator, based on the quantum walk in waveguides, on a commercial scale firstly, but there are still some problems such as input state, the structure and boundary of the waveguides that should be treated at present. A nearest-neighbor coupling model is used to deal with the question of coupled waveguides and an explicit analytical solution can be derived. Using the analytical solution, we analyze the effects of input state on particle number probability distribution function and the second-order coherence degree of the quantum walk process in periodic waveguides. The results show that the symmetry properties of the input state would influence the distribution of second-order coherence degree, but have little effect on the probability distribution function.