  We investigate quantum correlations in the ground state of noninteracting
Fermi gases of N particles trapped by an external space-dependent harmonic
potential, in any dimension. For this purpose, we compute one-particle
correlations, particle fluctuations and bipartite entanglement entropies of
extended space regions, and study their large-N scaling behaviors. The
half-space von Neumann entanglement entropy is computed for any dimension,
obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with
c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions
respectively. We show that the asymptotic large-N relation S_A\approx \pi^2
V_A/3, between the von Neumann entanglement entropy S_A and particle variance
V_A of an extended space region A, holds for any subsystem A and in any
dimension, analogously to homogeneous noninteracting Fermi gases.
