Perfect state transfer in Grover walks between states associated to vertices of a graph

• URL: http://arxiv.org/abs/2109.06418v1
• Date: Tue, 14 Sep 2021 03:59:47 GMT
• Title: Perfect state transfer in Grover walks between states associated to vertices of a graph
• Authors: Sho Kubota, Etsuo Segawa
• Abstract summary: We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. We call such states type states. We derive a necessary condition on eigenvalues of a graph for perfect state transfer between type states to occur.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer between vertex type states can be studied via Chebyshev polynomials. We derive a necessary condition on eigenvalues of a graph for perfect state transfer between vertex type states to occur. In addition, we perfectly determine the complete multipartite graphs whose partite sets are the same size on which perfect state transfer occurs between vertex type states, together with the time.

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