Concentration and purification of entanglement for qubit systems with ancillary cavity fields

We propose schemes for entanglement concentration and purification for qubit systems encoded in flying atomic pairs. We use cavity-quantum electrodynamics as an illustrative setting within which our proposals can be implemented. Maximally entangled pure states of qubits can be produced as a result of our protocols. In particular, the concentration protocol yields Bell states with the largest achievable theoretical probability while the purification scheme produces arbitrarily pure Bell states. The requirements for the implementation of these protocols are modest, within the state of the art, and we address all necessary steps in two specific setups based on experimentally mature microwave technology.