Efficient generation of N-photon binomial states and their use in quantum gates in cavity QED

A high-fidelity scheme to generate N-photon generalized binomial states (NGBSs) in a single-mode high-Q cavity is proposed. A method to construct superpositions of exact orthogonal NGBSs is also provided. It is then shown that these states, for any value of N, may be used for a realization of a controlled-NOT gate, based on the dispersive interaction between the cavity field and a control two-level atom. The possible implementation of the schemes is finally discussed.