  We propose the necessary and sufficient condition for the presence of quantum
entanglement in arbitrary symmetric pure states of two-level atomic systems. We
introduce a parameter to quantify quantum entanglement in such systems. We
express the inherent quantum fluctuations of a composite system of two-level
atoms as a sum of the quantum fluctuations of the individual constituent atoms
and their correlation terms. This helps to separate out and study solely the
quantum correlations among the atoms and obtain the criterion for the presence
of entanglement in such multiatomic systems.
