Characterization of a π-phase shift quantum gate for coherent-state qubits

We discuss the characterization of a pi-phase shift quantum gate acting on a qubit encoded in superpositions of coherent states. We adopt a technique relying on some a priori knowledge about the physics underlying the functioning of the device. A parameter summarizing the global quality of the quantum gate is obtained by 'virtually' processing an entangled state. With such an approach, we can facilitate the characterization of our gate, focusing on the useful subspace rather than on the entire phase space.