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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 bestdoi:10.1103/physrevlett.105.203601 pmid:21231232 fatcat:shjs2qcaczdrpo2b3wxh6lnj7q