We show that spin squeezing criteria commonly used for entanglement detection
can be erroneous, if the probe is not symmetric. We then derive a lower bound
on squeezing for separable states in spin systems probed asymmetrically. Using
this we further develop a procedure that allows us to verify the degree of
entanglement of a quantum state in the spin system. Finally, we apply our
method for entanglement verification to existing experimental data, and use it
to prove the existence of tri-partite entanglement in a spin squeezed atomic
ensemble.Comment: 7 pages, 2 figures (Include Supplemental material