A quantum network can be modeled by a graph G where the vertices correspond to the qubits and the
edges represent the interactions between them. Let G be a finite, simple and undirected graph with
adjacency matrix A. The continuous time quantum walk relative to A is defined by U(t) = exp (itA),
where t &isin R and i = &radic&minus1. The graph G is said to exhibit perfect pair state transfer (PPST) between
pairs of vertices (a, b) and (c, d) if there exists &tau &isin R such that U(&tau)(e_a&minuse_b) = &gamma(e_c&minuse_d), for some &gamma &isin
C. There is no perfect vertex state transfer in trees with more than three vertices. However, we find
all double subdivided stars T_{l,m} except P_6 exhibit PPST for every positive integer l and m. Also, we
observe that the evolution of certain pair states in a quantum network depends only on the local struc-
ture of the network, and it remains unchanged even if the global structure is altered. All graphs with
high fidelity vertex state transfer may be considered as isomorphic branches of the graph underlying
a large quantum network to exhibit high fidelity pair state transfer.

Keywords: Equitable partition, Perfect vertex state transfer, Perfect pair state transfer.