  Quantum state transfer and teleportation, with qubits encoded in internal
states of the atoms in cavities, among spatially separated nodes of a quantum
network in decoherence-free subspace are proposed, based on a cavity-assisted
interaction by single-photon pulses. We show in details the implementation of a
logic-qubit Hadamard gate and a two-logic-qubit conditional gate, and discuss
the experimental feasibility of our scheme.
