Fusing multiple W states simultaneously with a Fredkin gate

Abstract: We propose an optical scheme to prepare large-scale entangled networks of W states. The scheme works by simultaneously fusing three polarization-encoded W states of arbitrary size via accessing only one qubit of each W state. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in New J. Phys. 13, 103003 (2011)] and an H-polarized ancilla photon. Starting with three $n$-qubit W states, the scheme prepares a new W state with $3(n-1)$-qubits after postselection if both fusion gates operate successfully, i.e. a four-fold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large W states considerably when compared to previously reported schemes.