  For any mean value of a cartesian component of a spin vector we identify the
smallest possible uncertainty in any of the orthogonal components. The
corresponding states are optimal for spectroscopy and atomic clocks. We show
that the results for different spin J can be used to identify entanglement and
to quantity the depth of entanglement in systems with many particles. With the
procedure developed in this letter, collective spin measurements on an ensemble
of particles can be used as an experimental proof of multi-particle
entanglement
