| Summary: | Let A be the adjacency matrix of a graph G and suppose U(t) = exp(itA). We say that we have perfect state transfer in G from the vertex u to the vertex v at time t if there is a scalar γ of unit modulus such that U(t)eu = γ ev. It is known that perfect state transfer is rare. So C.Godsil gave a relaxation of this definition: we say that we have pretty good state transfer from u to v if there exists a complex number γ of unit modulus and, for each positive real ϵ there is a time t such that ‖U(t)eu–γ ev‖ < ϵ. In this paper, the quantum state transfer on 1-sum of star graphs Fk,l is explored. We show that there is no perfect state transfer on Fk,l, but there is pretty good state transfer on Fk,l if and only if k = l.
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