Spin squeezing inequalities and entanglement of $N$ qubit states

J. Korbicz, J. I. Cirac, M. Lewenstein

Published 2005-04-01, updated 2005-09-14Version 2

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 general states of $N$ qubits. Our inequalities have a clear physical interpretation as entanglement witnesses, can be relatively easy measured, and are given by complex, but {\it elementary} expressions.