New theory of diffusive and coherent nature of optical wave via a quantum walk

We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno, 2010), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature. •A relation between diffusive and coherent nature of wave is obtained.•A rigorous decoherent process is observed in quantum walk.•Quantum walk for a point-process is numerically considered.•Transfer matrix theory with S-matrix in optics is connected with quantum walk.