Deterministic protocol for mapping a qubit to coherent state superpositions in a cavity

We propose and analyze a quantum gate that transfers an arbitrary state of a qubit into a superposition of two quasiorthogonal coherent states of a cavity mode (qcMAP), with opposite phases. This qcMAP gate is based on conditional qubit and cavity operations exploiting the energy-level dispersive shifts in the regime where they are much stronger than the cavity and qubit linewidths. The generation of multicomponent superpositions of quasiorthogonal coherent states, nonlocal entangled states of two resonators, and multiqubit Greenberger-Horne- Zeilinger states can be efficiently achieved by this gate.