A complete set of generalized spin-squeezing inequalities is derived for an
ensemble of particles with an arbitrary spin. Our conditions are formulated
with the first and second moments of the collective angular momentum
coordinates. A method for mapping the spin-squeezing inequalities for spin-1/2
particles to entanglement conditions for spin-j particles is also presented. We
apply our mapping to obtain a generalization of the original spin-squeezing
inequality to higher spins. We show that, for large particle numbers, a
spin-squeezing parameter for entanglement detection based on one of our
inequalities is strictly stronger than the original spin-squeezing parameter
defined in [A. Sorensen et al., Nature 409, 63 (2001)]. We present a coordinate
system independent form of our inequalities that contains, besides the
correlation and covariance tensors of the collective angular momentum
operators, the nematic tensor appearing in the theory of spin nematics.
Finally, we discuss how to measure the quantities appearing in our inequalities
in experiments.Comment: 18 pages including 3 figures, revtex4; v2: references added, typos
corrected; v3: typos corrected, published versio
