Fusing multiple<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>W</mml:mi></mml:math>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 $3(n\ensuremath{-}1)$ 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.