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We use the "modes of the universe" approach to study a cavity-mediatedtwo-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. Weclarify 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 beenanticipated by other authors. We conclude that their proposed gate can workboth in the good and bad cavity limits, provided only that the pulses are longenough. Our formalism allows us to estimate analytically the size of thevarious error terms, and to follow the spectral evolution of the field + cavitysystem in the course of the interaction.

"Modes of the universe" study of two-photon deterministic, passive quantum logical gates