  (abridged) We investigate the quark deconfinement phase transition in the
context of binary neutron star (BNS) mergers. We employ a new
finite-temperature composition-dependent equation of state (EOS) with a first
order phase transition between hadrons and deconfined quarks to perform
numerical relativity simulations of BNS mergers. The softening of the EOS due
to the phase transition causes the merger remnants to be more compact and to
collapse to a black hole (BH) at earlier times. The phase transition is
imprinted on the postmerger gravitational wave (GW) signal duration, amplitude,
and peak frequency. However, this imprint is only detectable for binaries with
sufficiently long-lived remnants. Moreover, the phase transition does not
result in significant deviations from quasi-universal relations for the
postmerger GW peak frequency. We also study the impact of the phase transition
on dynamical ejecta, remnant accretion disk masses, r-process nucleosynthetic
yields and associated electromagnetic (EM) counterparts. While there are
differences in the EM counterparts and nucleosynthesis yields between the
purely hadronic models and the models with phase transitions, these can be
primarily ascribed to the difference in remnant collapse time between the two.
An exception is the non-thermal afterglow caused by the interaction of the
fastest component of the dynamical ejecta and the interstellar medium, which is
systematically boosted in the binaries with phase transition as a consequence
of the more violent merger they experience.
