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 S. K. Ozdemir et al., 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 fourfold coincidence at the detectors. The proposed scheme reduces the cost of creating arbitrarily large $W$ states considerably when compared to previously reported schemes.

• Received 12 February 2014

DOI:https://doi.org/10.1103/PhysRevA.89.042311