  The distance-inclination degeneracy limits gravitational-wave parameter
estimation of compact binary mergers. Although the degeneracy can be partially
broken by including higher-order modes or precession, these effects are
suppressed in binary neutron stars. In this work, we implement a new
parametrization of the tidal effects in the binary neutron-star waveform,
exploiting the binary Love relations, that breaks the distance-inclination
degeneracy. The binary Love relations prescribe the tidal deformability of a
neutron star as a function of its source-frame mass in an equation-of-state
insensitive way and, thus, allows direct measurement of the redshift of the
source. If the cosmological parameters are assumed to be known, the redshift
can be converted to a luminosity distance, and the distance-inclination
degeneracy can thus be broken. We implement this new approach, studying a range
of binary neutron-star observing scenarios using Bayesian parameter estimation
on synthetic data. In the era of the third-generation detectors, for
observations with signal-to-noise ratios ranging from 6 to 167, we forecast up
to an $\sim70\%$ decrease in the $90\%$ credible interval of the distance and
inclination and up to an $\sim50\%$ decrease in that of the source-frame
component masses. For edge-on systems, our approach can result in moderate
($\sim50\%$) improvement in the measurements of distance and inclination for
binaries with a signal-to-noise ratio as low as 10. This prescription can be
used to better infer the source-frame masses and, hence, refine population
properties of neutron stars, such as their maximum mass, impacting nuclear
astrophysics. When combined with the search for electromagnetic counterpart
observations, the work presented here can be used to put improved bounds on the
opening angle of jets from binary neutron-star mergers.
