  We quantify the information content of the non-linear matter power spectrum,
the halo mass function, and the void size function, using the Quijote N-body
simulations. We find that these three statistics exhibit very different
degeneracies amongst the cosmological parameters, and thus the combination of
all three probes enables the breaking of degeneracies, in turn yielding
remarkably tight constraints. We perform a Fisher analysis using the full
covariance matrix, including all auto- and cross-correlations, finding that
this increases the information content for neutrino mass compared to a
correlation-free analysis. The multiplicative improvement of the constraints on
the cosmological parameters obtained by combining all three probes compared to
using the power spectrum alone are: 137, 5, 8, 20, 10, and 43, for $\Omega_m$,
$\Omega_b$, $h$, $n_s$, $\sigma_8$, and $M_\nu$, respectively. The marginalized
error on the sum of the neutrino masses is $\sigma(M_\nu)=0.018\,{\rm eV}$ for
a cosmological volume of $1\,(h^{-1}{\rm Gpc})^3$, using $k_{\max}=0.5\,h{\rm
Mpc}^{-1}$, and without CMB priors. We note that this error is an underestimate
insomuch as we do not consider super-sample covariance, baryonic effects, and
realistic survey noises and systematics. On the other hand, it is an
overestimate insomuch as our cuts and binning are suboptimal due to
restrictions imposed by the simulation resolution. Given upcoming galaxy
surveys will observe volumes spanning $\sim 100\,(h^{-1}{\rm Gpc})^3$, this
presents a promising new avenue to measure neutrino mass without being
restricted by the need for accurate knowledge of the optical depth, which is
required for CMB-based measurements. Furthermore, the improved constraints on
other cosmological parameters, notably $\Omega_m$, may also be competitive with
CMB-based measurements.
