Fusing multiple W states simultaneously with a Fredkin gate

Abstract

We propose an optical scheme to prepare large-scale entangled networks ofWstates. The scheme works by simultaneously fusing three polarization-encodedWstates of arbitrary size via accessing only one qubit of eachWstate. It is composed of a Fredkin gate (controlled-swap gate), two fusion gates [as proposed in S. K. Ozdemiret al.,New J. Phys.13, 103003 (2011)], and anH-polarized ancilla photon. Starting with threen-qubitWstates, the scheme prepares a newWstate with3(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 largeWstates considerably when compared to previously reported schemes.