  Let $L$ denote the Laplacian matrix of a graph $G$. We study continuous
quantum walks on $G$ defined by the transition matrix
$U(t)=\exp\left(itL\right)$. The initial state is of the pair state form,
$e_a-e_b$ with $a,b$ being any two vertices of $G$. We provide two ways to
construct infinite families of graphs that have perfect pair transfer. We study
a "transitivity" phenomenon which cannot occur in vertex state transfer. We
characterize perfect pair state transfer on paths and cycles. We also study the
case when quantum walks are generated by the unsigned Laplacians of underlying
graphs and the initial states are of the plus state form, $e_a+e_b$. When the
underlying graphs are bipartite, plus state transfer is equivalent to pair
state transfer.
