Polarization entanglement purification of nonlocal microwave photons based on the cross-Kerr effect in circuit QED

Microwave photons have become very important qubits in quantum communication as the first quantum satellite has been launched successfully. Therefore, it is a necessary and meaningful task for ensuring the high security and efficiency of microwave quantum communication in practice. Here, we present an original polarization entanglement purification protocol (EPP) for nonlocal microwave photons based on the cross-Kerr effect in circuit quantum electrodynamics (QED). Our protocol can solve the problem that the purity of maximally entangled states used for constructing quantum channel will decrease due to decoherence from environment noise. This task is accomplished by means of the polarization parity-check quantum nondemolition (QND) detector, the bit-flipping operation, and the linear microwave elements. The QND detector is composed of several cross-Kerr effect systems which can be realized by coupling two superconducting transmission line resonators to a superconducting molecule with the N-type level structure. Our calculation shows that the QND detector has a high fidelity with applicable experimental parameters in circuit QED, which means this EPP can succeed with a high fidelity and has good applications in long-distance quantum communication assisted by microwave photons in the future, such as satellite quantum communication.