  In this paper, we explore the prospect for improving the measurement accuracy
of masses and radii of neutron stars. We consider imminent and long-term
upgrades of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and
Virgo, as well as next-generation observatories -- the Cosmic Explorer and
Einstein Telescope. We find that neutron star radius with single events will be
constrained to within roughly 500m with the current generation of detectors and
their upgrades. This will improve to 200m, 100m and 50m with a network of
observatories that contain one, two or three next-generation observatories,
respectively. Combining events in bins of 0.05 solar masses we find that for
stiffer (softer) equations-of-state like ALF2 (APR4), a network of three XG
observatories will determine the radius to within 30m (100m) over the entire
mass range of neutron stars from 1 to 2.0 solar masses (2.2 solar masses),
allowed by the respective equations-of-state. Neutron star masses will be
measured to within 0.5 percent with three XG observatories irrespective of the
actual equation-of-state. Measurement accuracies will be a factor of 4 or 2
worse if the network contains only one or two XG observatories, respectively,
and a factor of 10 worse in the case of networks consisting of Advanced LIGO,
Virgo KAGRA and their upgrades. Tens to hundreds of high-fidelity events
detected by future observatories will allow us to accurately measure the
mass-radius curve and hence determine the dense matter equation-of-state to
exquisite precision.
