Comparative model study of two-photon deterministic passive quantum logical gates

We use the 'modes of the universe' approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka, and Nakamura. We clarify the relationship between the more commonly used input-output formalism and that of Koshino et al. and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms and to follow the spectral evolution of the field+cavity system in the course of the interaction.