Survival probability of the Grover walk on the ladder graph
arXiv:2205.13188 · doi:10.1088/1751-8121/accfd4
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 Mare\v s et al., Phys. Rev. A 101, 032113 (2020), 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 , 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 can change from increasing and converging exponentially quickly to decreasing and converging like 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.
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