Spin Squeezing Inequalities and Entanglement of $N$ Qubit States

We derive spin squeezing inequalities that generalize the concept of the spin squeezing parameter and provide necessary and sufficient conditions for genuine 2-, or 3-qubit entanglement for symmetric states, and sufficient condition for $N$-qubit states. Our inequalities have a clear physical interpretation as entanglement witnesses, can be easily measured, and are given by complex but elementary expressions.