Enhancing the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-state quantum-network-fusion process with a single Fredkin gate

Abstract

Integrating a single Fredkin (controlled swap) gate to the previously introduced $W$ state fusion mechanism [Ozdemir et al., New J. Phys. 13, 103003 (2011)] and using an ancillary photon, we increase the size of the fused $W$ states and essentially, we improve the success probability of the fusion process in a promising way for a possible deterministic $W$-state fusion mechanism. Besides fusing arbitrary size $W$ states, our setup can also fuse Bell states to create $W$ states with a success probability $3/4$ which is much higher than the previous works. Therefore using only this setup, it is now possible to start with Bell pairs to create and expand arbitrary size $W$ states. Since a higher probability of success implies a lower cost of resource in terms of the number of the states spent to achieve a target size, our setup gives rise to more cost-efficient scenarios.