We present a theoretical proposal for a physical implementation of entanglement concentration and purification protocols for two-mode squeezed microwave photons in circuit quantum electrodynamics(QED). First, we give the description of the cross-Kerr effect induced between two resonators in circuit QED. Then we use the cross-Kerr media to design the effective quantum nondemolition (QND) measurement on microwave-photon number. By using the QND measurement, the parties in quantum communication can accomplish the entanglement concentration and purification of nonlocal two-mode squeezed microwave photons. We discuss the feasibility of our schemes by giving the detailed parameters which can be realized with current experimental technology. Our work can improve some practical applications in continuous-variable microwave-based quantum information processing.
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 meaningfultask 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.