Multiparticle covariance matrices and the impossibility of detecting graph-state entanglement with two-particle correlations
Oleg Gittsovich, Philipp Hyllus, Otfried Gühne · Physical Review A · 2010
We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows detection of bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the Greenberger-Horne-Zeilinger (GHZ) states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states to which the GHZ states belong.