In practice, single photons are generated as a mixture of vacuum with a single photon with weights 1-p and p, respectively; here we are concerned with increasing p by directing multiple copies of the single photon-vacuum mixture into a linear optic device and applying photodetection on some outputs to conditionally prepare single photon states with larger p. We prove that it is impossible, under certain conditions, to increase p via linear optics and conditional preparation based on photodetection, and we also establish a class of photodetection events for which p can be improved. In addition we prove that it is not possible to obtain perfect (p=1) single photon states via this method from imperfect (p<1) inputs.
@article{arxiv.quant-ph/0309140,
title = {On improving single photon sources via linear optics and photodetection},
author = {Dominic W. Berry and Stefan Scheel and Barry C. Sanders and Peter L. Knight},
journal= {arXiv preprint arXiv:quant-ph/0309140},
year = {2007}
}