An optical fusion gate for W-states

We introduce a simple optical gate to fuse arbitrary size polarization entangled W-states to prepare larger W-states. The gate requires a polarizing beam splitter (PBS), a half wave plate (HWP) and two photon detectors. We study numerically and analytically the necessary resource consumption for preparing larger W-states by fusing smaller ones with the proposed fusion gate. We show analytically that resource requirement scales at most sub-exponentially with the increasing size of the state to be prepared. We numerically determine the resource cost for fusion without recycling where W-states of arbitrary size can be optimally prepared. Moreover, we introduce another strategy which is based on recycling and outperforms the optimal strategy for non-recycling case.