We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.
@article{arxiv.1004.0608,
title = {Optimal local expansion of W states using linear optics and Fock states},
author = {Rikizo Ikuta and Toshiyuki Tashima and Takashi Yamamoto and Masato Koashi and Nobuyuki Imoto},
journal= {arXiv preprint arXiv:1004.0608},
year = {2011}
}