Quantum Pair State Transfer on Isomorphic Branches

Quantum state transfer plays an important role in quantum information processing. The evolution of certain pair states in a quantum network with Heisenberg $XY$ Hamiltonian depends only on the local structure 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. Among other graphs, one may construct infinite family of trees admitting perfect pair state transfer.