Directivity of quantum walk via its random walk replica

Abstract

A quantum walk exhibits quite different properties compared to a classical random walk, such as linear spreading and localization. While quantum superposition provides these interesting properties, their intuitive understanding and characterization are not easy. In this paper, we construct one-dimensional random walks derived by the time evolution of quantum walks and prove that the probability distribution of the original quantum walk and that of the corresponding quantum-walkreplicating random walk is equivalent. Moreover, we demonstrate further insights through the analysis of quantum-walk-replicating random walks, such as the manifestation of linear spreading and localization, by visualizing the traces of individual walkers and transition probabilities.