Detection and characterization of multipartite entanglement in optical lattices

We investigate the detection and characterization of entanglement based on the quantum network introduced in Phys. Rev. Lett. 93, 110501 (2004) for different experimental scenarios. We first give a detailed discussion of the ideal scheme where no errors are present and full spatial resolution is available. Then we analyze the implementation of the network in an optical lattice. We find that even without any spatial resolution entanglement can be detected and characterized in various kinds of states including cluster states and macroscopic superposition states. We also study the effects of detection errors and imperfect dynamics on the detection network. For our scheme to be practical these errors have to be on the order of one over the number of investigated lattice sites. Finally, we consider the case of limited spatial resolution and conclude that significant improvement in entanglement detection and characterization compared to having no spatial resolution is only possible if single lattice sites can be resolved.