Simultaneous quantum state exchange or transfer between two sets of cavities via a superconducting coupler qubit

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. 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. The method can be generalized to other systems by using different types of physical qubit as a coupler to accomplish the same task.