  We propose an approach to simultaneously perform quantum state exchange or
transfer between two sets of cavities, each containing $N$ cavities, by using
only one superconducting coupler qubit. The quantum states to be exchanged or
transferred can be arbitrary pure or mixed states and entangled or
nonentangled. The operation time does not increase with the number of cavities,
and there is no need of applying classic pulses during the entire operation.
Moreover, the approach can be also applied to realize quantum state exchange or
transfer between two sets of qubits, such as that between two multi-qubit
quantum registers. We further show that the present proposal can be used to
simultaneously generate multiple Einstein-Podolsky-Rosen pairs of photons or
qubits, which are important in quantum communication. The method can be
generalized to other systems by using different types of physical qubit as a
coupler to accomplish the same task.
