Elementary optical gate for expanding an entanglement web

We introduce an elementary optical gate for expanding polarization entangled W states in which every pair of photons is entangled alike. The gate is composed of a pair of 50:50 beamsplitters and ancillary photons in the two-photon Fock state. By seeding one of the photons in an n-photon W state into this gate, we obtain an (n+2)-photon W state after postselection. This gate gives a better efficiency and a simpler implementation than previous proposals for W-state preparation.