Preparation of multipartite entangled states and one-step implementation of 1 → M economical phase-covariant quantum anti-cloning in cavity QED

The scheme for preparing a multipartite entangled state and implementing 1 -> M economical phase-covariant quantum anti-cloning only by one step are proposed. By using the symmetric and asymmetric interactions between N atoms and the cavity, N-particle Greenberger-Horne-Zeilinger (GHZ) and W states are prepared, respectively. Furthermore, a scheme of 1 -> M anti-cloning is also proposed through preparing the W state. The decoherence from atomic spontaneous emission is negligible due to the excited state of the atom being adiabatically eliminated under large detuning. The scheme is insensitive to the cavity decay due to the cavity only being virtually excited. The experimental feasibility of the present scheme is also discussed.