  We propose an entanglement purification scheme based on material qubits and
ancillary coherent multiphoton states. We consider a typical QED scenario where
material qubits implemented by two-level atoms fly sequentially through a
cavity and interact resonantly with a single mode of the radiation field. We
explore the theoretical possibilities of realizing a high-fidelity two-qubit
quantum operation necessary for the purification protocol with the help of a
postselective balanced homodyne photodetection. We demonstrate that the
obtained probabilistic quantum operation can be used as a bilateral operation
in the proposed purification scheme. It is shown that the probabilistic nature
of this quantum operation is counterbalanced in the last step of the scheme
where qubits are not discarded after inadequate qubit measurements. As this
protocol requires present-day experimental setups and generates high-fidelity
entangled pairs with high repetition rates, it may offer interesting
perspectives for applications in quantum information theory.
