  We answer the question whether linear-optical processing of the states
produced by one or multiple imperfect single-photon sources can improve the
single-photon fidelity. This processing can include arbitrary interferometers,
coherent states, feedforward, and conditioning on results of detections. We
show that without introducing multiphoton components, the single-photon
fraction in any of the single-mode states resulting from such processing cannot
be made to exceed the efficiency of the best available photon source. If
multiphoton components are allowed, the single-photon fidelity cannot be
increased beyond 1/2. We propose a natural general definition of the
quantum-optical state efficiency, and show that it cannot increase under
linear-optical processing.
