  We investigate the 2D weakly interacting Bose-Einstein condensate in a
rotating trap by the tools of quantum information theory. The critical
exponents of the ground state fidelity susceptibility and the correlation
length of the system are obtained for the quantum phase transition when the
frst vortex is formed. We also find the single-particle entanglement can be an
indicator of the angular momentums for some real ground states. The
single-particle entanglement of fractional quantum Hall states such as Laughlin
state and Pfaffian state is also studied.
