Cluster state entanglement generation and concentration on nitrogen-vacancy centers in decoherence-free subspace

Exploiting the composite system in which two nitrogen-vacancy centers coupled to a microtoroid resonator, we proposed the cluster state entanglement generation and concentration schemes on nitrogen-vacancy centers in decoherence-free subspace. The proposed system is well suited for the systematic preparation of cluster states in one-way quantum computation due to the controllability and scalability. Accompanied with the optimal entanglement concentration protocol for the logic-qubit expanded cluster state, one can efficiently preserve the maximal entanglement. We discussed the experimental feasibility of our schemes by considering the currently available techniques, and believe that the schemes may be useful in further solid-state quantum information processing.