Multipartite polariton entanglement in semiconductor microcavities

We study the entanglement of multiple polariton modes, which results in continuous variable cluster states suitable for quantum computation. Schemes are based on parametric scattering between spin-polarized lower and upper polariton branches in planar microcavities or spin-polarized orbital angular momentum states in mesa structures. Such systems are modeled by numerical solution of truncated density matrices and compared to the solution of the Heisenberg equations for the set of field correlators up to third order. Four-body entanglement is evidenced by violation of the van Loock-Furusawa quadripartite inequalities. We show that the entanglement is able to withstand a realistic strength of pure dephasing present in typical systems.