Photon counting schemes and performance of non-deterministic nonlinear gates in linear optics

The performance of nondeterministic nonlinear gates in linear optics relies on the photon counting scheme being employed and the efficiencies of the detectors in such schemes. We assess the performance of the nonlinear sign gate, which is a critical component of linear optical quantum computing, for two standard photon counting methods: the double detector array and the visible light photon counter. Our analysis shows that the double detector array is insufficient to provide the photon counting capability for effective nondeterministic nonlinear transformations, and we determine the gate fidelity for both photon counting methods as a function of detector efficiencies.