  Given an action of a compact quantum group on a unital C*-algebra, one can
amplify the action with an adjoint representation of the quantum group on a
finite dimensional matrix algebra, and consider the resulting inclusion of
fixed point algebras. We show that this inclusion is a finite index inclusion
of C*-algebras when the quantum group acts freely. We show that two natural
definitions for a quantum group to act freely, namely the Ellwood condition and
the saturatedness condition, are equivalent.
