Dynamical properties and applications of discrete time nonunitary quantum walks

Most existing studies of quantum walk focus on unitary closed systems, while the nonunitary counterpart, relevant to open quantum systems, remains relatively unexplored. This paper analyzes the position distribution and variance of quantum walk under the specific nonunitary evolution operator. Our results reveal that the variance exhibits distinct dynamical behavior depending on angular parameters, spatial dimensions, and initial states. In particular, for the one-dimensional non-Hermitian two-band lattice model, we demonstrate that the variance grows quadratically with time steps in the short-time regime, indicating faster diffusion than classical random walk. Leveraging this acceleration, we further propose a teleportation protocol based on nonunitary quantum walk, which eliminates the need for entangled state preparation and thereby reduces resource overhead while enhancing information transfer efficiency.