  We investigate observable signatures of a first-order quantum chromodynamics
(QCD) phase transition in the context of core collapse supernovae. To this end,
we conduct axially symmetric numerical relativity simulations with multi-energy
neutrino transport, using a hadron-quark hybrid equation of state (EOS). We
consider four non-rotating progenitor models, whose masses range from $9.6$ to
$70$ M$_\odot$. We find that the two less massive progenitor stars (9.6 and
11.2 M$_\odot$) show a successful explosion, which is driven by the neutrino
heating. They do not undergo the QCD phase transition and leave behind a
neutron star (NS). As for the more massive progenitor stars (50 and 70
M$_\odot$), the proto-neutron star (PNS) core enters the phase transition
region and experiences the second collapse. Because of a sudden stiffening of
the EOS entering to the pure quark matter regime, a strong shock wave is formed
and blows off the PNS envelope in the 50 M$_\odot$ model. Consequently, the
remnant becomes a quark core surrounded by hadronic matters, leading to the
formation of the hybrid star. However for the 70 M$_\odot$ model, the shock
wave cannot overcome the continuous mass accretion and it readily becomes a
black hole. We find that the neutrino and gravitational wave (GW) signals from
supernova explosions driven by the hadron-quark phase transition are detectable
for the present generation of neutrino and GW detectors. Furthermore, the
analysis of the GW detector response reveals unique kHz signatures, which will
allow us to distinguish this class of supernova explosions from failed and
neutrino-driven explosions.
