  Using full 3+1 dimensional general-relativistic hydrodynamic simulations of
equal- and unequal-mass neutron-star binaries with properties that are
consistent with those inferred from the inspiral of GW170817, we perform a
detailed study of the quark-formation processes that could take place after
merger. We use three equations of state consistent with current pulsar
observations derived from a novel finite-temperature framework based on V-QCD,
a non-perturbative gauge/gravity model for Quantum Chromodynamics. In this way,
we identify three different post-merger stages at which mixed baryonic and
quark matter, as well as pure quark matter, are generated. A phase transition
triggered collapse already $\lesssim 10\,\rm{ms}$ after the merger reveals that
the softest version of our equations of state is actually inconsistent with the
expected second-long post-merger lifetime of GW170817. Our results underline
the impact that multi-messenger observations of binary neutron-star mergers can
have in constraining the equation of state of nuclear matter, especially in its
most extreme regimes.
