Local expansion of photonic W state using a polarization dependent beamsplitter

We propose a simple probabilistic optical gate to expand polarization entangled W states. The gate uses one polarization-dependent beamsplitter and a horizontally polarized single photon as an ancilla. The gate post-selectively expands $N$-photon W states to $(N+1)$-photon W states. A feasibility analysis considering the realistic experimental conditions show that the scheme is within the reach of the current quantum optical technologies.