  Elementary particles such as quarks and gluons are expected to be fundamental
degrees of freedom at ultra high temperatures or densities, while natural
phenomena in our daily lives are described in terms of hadronic degrees of
freedom. Massive neutron stars and remnants of binary neutron star mergers may
contain quark matter, but it is not known how the transition from hadron matter
to quark matter occurs. Different transition scenarios predict different
gravitational waveforms emitted from binary neutron star mergers. If the
difference between the equations of state occurs at sufficiently high density,
it is expected that the difference between waveforms mainly appears in the
merger or the post-merger phase rather than in the inspiral phase. The typical
frequency of gravitational waves after the coalescence is higher than 2 kHz,
which is difficult to observe using current detectors. In this study, we
performed Bayesian model selection for two representative scenarios and
investigated whether observations with future detectors will allow us to
identify the correct model. We assume that the relatively low density equation
of state around the nuclear saturation density is completely known from
accumulated observations. Under this assumption, we find that it is reasonable
to expect to be able to identify the correct transition scenario with
third-generation detectors or specialized detectors with high sensitivity at
high frequencies designed for post-merger signal observation, e.g., NEMO.
