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 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.