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

TL;DR

This paper analyzes a cavity-mediated two-photon quantum gate using the 'modes of the universe' approach, clarifying its relationship with existing formalisms and demonstrating its effectiveness across different cavity regimes.

Contribution

It introduces an analytical formalism to evaluate the spectral evolution and error terms of the two-photon gate, extending understanding of its operational limits.

Findings

The gate functions in both good and bad cavity regimes with sufficiently long pulses.

The formalism provides analytical estimates of error sizes.

The study clarifies the relationship between different theoretical approaches.

Abstract

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.