  We study quantum phase transitions involving fractional quantum Hall states,
using numerical calculations of entanglements and related quantities. We tune
finite-size wavefunctions on spherical geometries, by varying the interaction
potential away from the Coulomb interaction. We uncover signatures of quantum
phase transitions contained in the scaling behavior of the entropy of
entanglement between two parts of the sphere. In addition to the entanglement
entropy, we show that signatures of quantum phase transitions also appear in
other aspects of the reduced density matrix of one part of the sphere.
