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We extend the criteria for $k$-particle entanglement from the spin squeezingparameter presented in [A.S. S{\o}rensen and K. M{\o}lmer, Phys. Rev. Lett.{\bf 86}, 4431 (2001)] to systems with a fluctating number of particles. Wealso discuss how other spin squeezing inequalities can be generalized to thissituation. Further, we give an operational meaning to the bounds for caseswhere the individual particles cannot be addressed. As a by-product, thisallows us to show that in spin squeezing experiments with cold gases theparticles are typically distinguishable in practise. Our results justify theapplication of the S{\o}rensen-M{\o}lmer bounds in recent experiments on spinsqueezing in Bose-Einstein condensates.

Entanglement and Extreme Spin Squeezing for a Fluctuating Number of Indistinguishable Particles