Detecting multiparticle entanglement with spin squeezing inequalities.

G. Tóth^a,b,c, G. Vitagliano^a

^aDepartment of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain

^bIKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain

^cWigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

We study the problem of detecting entanglement and its depth in systems composed of very many particles. We derive entanglement criteria based only on few easy measurable quantities such as the mean values and variances of collective spin components. In particular we present what we call a generalized spin squeezing parameter, that can be used to detect a class of states wider than the spin squeezed states. Moreover we present a criterion to estimate the entanglement depth that outperforms previous well-known criteria. It has been used in a recent experiment to prove that the produced Dicke-like state had an entanglement depth of at least 28 particles.