Effective preparation of the N-dimension spin Greenberger-Horne-Zeilinger state with quantum dots embedded inmicrocavities

We propose a scheme for preparation of the N-dimension spin Greenberger-Horne-Zeilinger state by exploiting quantum dots (QDs) embedded in microcavities. Numerically analysed results show that with the spin-selective photon reflection from the cavity, we can complete the scheme assisted by one polarized photon with high fidelity and 100% successful probability in principle. Furthermore, the set-up is just composed of simple linear optical elements, delay lines and conventional photon detectors, which are feasible with existing experimental technology. Moreover, QDs have numerous admirable features in weak-coupling regime, which are practicable in realistic cavity quantum electrodynamics system shown by previous numerical simulations and experiments. Therefore, our scheme might be realized in near future.