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We present a novel semi-analytical methodology to construct optimal linearoptical circuits for heralded production of 3-photon GHZ and 2-photon Bellstates. We provide a detailed description and analysis of the resulting opticalschemes, which deliver success probabilities of 1/54 and 2/27 for dual-railencoded 3-GHZ and Bell states generation, respectively. Our results improve theknown constructive bounds on the success probabilities for 3-GHZ states and areof particular importance for a ballistic quantum computing model, for whichthese states provide an essential resource.

Improved Heralded Schemes to Generate Entangled States From Single Photons