  Explosive astrophysical systems, such as supernovae or compact star binary
mergers, provide conditions where strange quark matter can appear. The high
degree of isospin asymmetry and temperatures of several MeV in such systems may
cause a transition to the quark phase already around saturation density.
Observable signals from the appearance of quark matter can be predicted and
studied in astrophysical simulations. As input in such simulations, an equation
of state with an integrated quark matter phase transition for a large
temperature, density and proton fraction range is required. Additionally,
restrictions from heavy ion data and pulsar observation must be considered. In
this work we present such an approach. We implement a quark matter phase
transition in a hadronic equation of state widely used for astrophysical
simulations and discuss its compatibility with heavy ion collisions and pulsar
data. Furthermore, we review the recently studied implications of the QCD phase
transition during the early post-bounce evolution of core-collapse supernovae
and introduce the effects from strong interactions to increase the maximum mass
of hybrid stars. In the MIT bag model, together with the strange quark mass and
the bag constant, the strong coupling constant $\alpha_s$ provides a parameter
to set the beginning and extension of the quark phase and with this the mass
and radius of hybrid stars.
