In the interior of supernovae, temperatures and densities exceed the range that is easily accessible by terrestrial experiments. With the improving sensitivities of neutrino and gravitational wave detectors, the chance of obtaining observations providing a deep view into the heart of a close-by supernova explosion is steadily increasing. Based on computational models we investigate the imprint of the nuclear equation of state on the emission of neutrinos and gravitational waves. If a QCD phase transition to quark matter occurs during the immediate postbounce accretion phase, a strong second shock front is formed at a radius of order 10 km. Neutronised hadronic outer layers of the protoneutron star fall into it, are shock-heated and lead to a rapid acceleration of the second shock wave. As soon as this shock reduces the electron degeneracy at the neutrinospheres, a sharp second neutrino burst is emitted, dominated by electron antineutrinos. Together with the abruptly increasing mean energies of μ- and τ-neutrinos it may serve as a clear signature of the phase transition of the protoneutron star core to a more compact state.