Two schemes for generating four-photon cluster states based on quantum dot microcavity coupling systems

We propose two schemes that generate four-photon cluster states based on quantum dot microcavity coupling systems. In the first scheme, the four-photon cluster state is generated from four single-photon states assisted by three quantum dot nondemolition detectors. In the second scheme, a photon polarization controlled-Z (C-Z) gate is constructed firstly by exploiting a quantum dot microcavity coupling system, and then the four-photon cluster state is generated from two EPR pairs, which come from currently available spontaneous parametric down-conversion technique. Both nondemolition detectors and a photon polarization C-Z gate are realized by quantum dot microcavity coupling systems, which can be realized with near unity success probability and nearly perfect fidelity as the side leakage rate is small and the coupling strength is strong.