Entanglement concentration for multi-particle partially entangled W state using nitrogen vacancy center and microtoroidal resonator system

In this paper, we present an efficient entanglement concentration protocol (ECP) for N spatially separated nitrogen-vacancy (N-V) centers coupled to microtoroidal resonators in a partially entangled W state. The robustness of W-type entanglement contrasts strongly with the Greenberger-Horne-Zeilinger (GHZ) state which is fully separable after loss of one qubit. We construct the parity-check gate by introducing an auxiliary N-V center in microcavity and a single photon. Based on the parity-check measurement and local operations, the remote parities can distill a maximally entangled W state from a partially entangled state with a certain success probability. By iterating the concentration process several times, the present ECP can obtain an optimal yield. With its robustness and scalability, the present ECP for entangled N-V center ensembles can be widely applied to quantum repeaters and long-distance quantum communications.