  We provide an in-depth characterization of a three modes Bose-Einstein
condensate trapped in a symmetric circular triple well potential. We analyze
how a subsystem independent measure of entanglement, the purity related to the
su(3) algebra, scales for increasing number of atoms and signals correctly the
quantum phase transition between two dynamical regimes in a specific
arrangement. Moreover, this measure, which is intrinsically related to particle
entanglement, also depicts if some squeezing is occurring when we consider the
system's ground state.
