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.

Figure 1

(Color online) (a) Local extension of $W$ states. (b) The proposed optical gate $\left(T_{+2}^W\right)$ converts $\mid W_N⟩$ to $\mid W_{N+2}⟩$. (c) If a photon in state $\mid 1⟩$ is seeded, the gate produces $\mid W_3⟩$. (d) If we start with two photons in state $(\mid 01⟩+\mid 10⟩)∕\sqrt{2}$, we obtain $\mid W_4⟩$.

Figure 2

(Color online) The schematic diagram of the setup for $T_{+2}^W$ gate.