Triggered single-photon sources produce the vacuum state with nonzero probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states with probabilities 1 − p and p, respectively. Here we are concerned with increasing the efficiency p by directing multiple copies of the single-photon-vacuum mixture into a linear optical device and applying photodetection on some outputs. We prove that it is impossible, under certain conditions, to increase p via linear optics and conditional preparation based on photodetection. We also establish a class of photodetection events for which p can be improved, although with an added multiphoton component. In addition we prove that it is not possible to obtain perfect single-photon states via this method from imperfect ͑p Ͻ 1͒ inputs. . Although these sources do not have as high a fidelity as can be achieved using parametric downconversion [4], they have the advantage that they are triggered. For a triggered single-photon source, the probability of more than one photon being produced is much lower than that for a Poissonian process [10], but the vacuum contribution can be quite high. That is, the coefficients q n of the single-mode output field density matrix ͚ n q n ͉n͗͘n͉ are negligible for n ജ 2, but the vacuum contribution q 0 is substantial. For this study we consider an ideal single-mode singlephoton source with limited efficiency p, which may be represented by the density operatorIncreasing the efficiency p is important because of requirements for quantum optics experiments, especially those concerned with quantum information processing. Much of this effort is directed to improving sources, but here we pose the question as to whether it is possible to perform postprocessing to obtain higher efficiency, while maintaining a negligible multiphoton contribution. A promising method of postprocessing is via linear optics and photodetection. It has been shown that linear optics and photodetection can be used to perform quantum computation ͓2͔, and optical controlled- NOT Below we show that it is impossible to increase the single-photon efficiency p, provided we consider detection results where all but one of the photons are detected. This eliminates the most straightforward possibility for ensuring that the multiphoton contribution is negligible. If we allow other detection results, we show it is possible for lowefficiency (small p) single-photon states to yield, via linear optics and conditional preparation based on photodetection, an output with a larger probability for a single photon. However, these schemes also yield multiphoton contributions comparable to the Poisson distribution.In the general case we start with a supply of N mixed states of the form (1). For additional generality we allow the different inputs to have different probabilities for a single photon, p i , and we denote the maximum of these probabilities by p max . The initial input stat...
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