  With an average density higher than the nuclear density, neutron stars (NS)
provide a unique test-ground for nuclear physics, quantum chromodynamics (QCD),
and nuclear superfluidity. Determination of the fundamental interactions that
govern matter under such extreme conditions is one of the major unsolved
problems of modern physics, and -- since it is impossible to replicate these
conditions on Earth -- a major scientific motivation for SKA. The most
stringent observational constraints come from measurements of NS bulk
properties: each model for the microscopic behaviour of matter predicts a
specific density-pressure relation (its `Equation of state', EOS). This
generates a unique mass-radius relation which predicts a characteristic radius
for a large range of masses and a maximum mass above which NS collapse to black
holes. It also uniquely predicts other bulk quantities, like maximum spin
frequency and moment of inertia. The SKA, in Phase 1 and particularly in Phase
2 will, thanks to the exquisite timing precision enabled by its raw
sensitivity, and surveys that dramatically increase the number of sources: 1)
Provide many more precise NS mass measurements (high mass NS measurements are
particularly important for ruling out EOS models); 2) Allow the measurement of
the NS moment of inertia in highly relativistic binaries such as the Double
Pulsar; 3) Greatly increase the number of fast-spinning NS, with the potential
discovery of spin frequencies above those allowed by some EOS models; 4)
Improve our knowledge of new classes of binary pulsars such as black widows and
redbacks (which may be massive as a class) through sensitive broad-band radio
observations; and 5) Improve our understanding of dense matter superfluidity
and the state of matter in the interior through the study of rotational
glitches, provided that an ad-hoc campaign is developed.
