Quantum Information Processing using coherent states in cavity QED

Using the highly detuned interaction between three-level $\Lambda$-type atoms and coherent optical fields, we can realize the C-NOT gates from atoms to atoms, optical fields to optical fields, atoms to optical fields and optical fields to atoms. Based on the realization of the C-NOT gates we propose an entanglement purification scheme to purify a mixed entangled states of coherent optical fields. The simplicity of the current scheme makes it possible that it will be implemented in experiment in the near future.