Survival probability of the Grover walk on the ladder graph
Etsuo Segawa, Shigeyuki Koyama, Norio Konno, M. Štefaňák · Journal of Physics A Mathematical and Theoretical · 2023
Abstract We provide a detailed analysis of the survival probability of the Grover walk on the ladder graph with an absorbing sink. This model was discussed in Mareš et al (2020 Phys. Rev. A 101 032113 ), as an example of counter-intuitive behaviour in quantum transport where it was found that the survival probability decreases with the length of the ladder L , despite the fact that the number of dark states increases. An orthonormal basis in the dark subspace is constructed, which allows us to derive a closed formula for the survival probability. It is shown that the course of the survival probability as a function of L can change from increasing and converging exponentially quickly to decreasing and converging like L −1 simply by attaching a loop to one of the corners of the ladder. The interplay between the initial state and the graph configuration is investigated.