Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. We describe a method for increasing the probability of a single photon via a chain of beam splitters. This method has the drawbacks that it introduces a significant multiphoton component, and it can not be used to increase the probability for a single photon above 1/2. Part of the reason for these drawbacks is the incoherence in the photon sources. If the photon sources produced pure states rather than incoherent superpositions, it would be possible to obtain a perfect single photon output. The method for incoherent inputs is robust against detector inefficiencies, but sensitive to dark counts and the multiphoton component in the input.
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