Negative Correlations and Entanglement in Higher-Spin Dicke States

Abstract

We consider entanglement criteria based on the spin squeezing inequalities for arbitrary spin systems. Here we use the negative correlations to detect the entanglement in the system with exchange symmetry. For arbitrary spin systems, we can find that the state is entangled, when the minimal pairwise correlation is negative. Then we give a parameter which is defined by the collective angular momentum operator, to detect the entanglement for the Dicke state with N spin −1 particles, and the results are as the same as negative correlation. We also consider the directions of negative correlation, the state is entangled in two orthogonal directions for the superposition of Dicke state without parity.