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We study the detectability of postmerger QCD phase transitions in neutronstar binaries with next-generation gravitational-wave detectors Cosmic Explorerand Einstein Telescope. We perform numerical relativity simulations of neutronstar mergers with equations of state that include a quark deconfinement phasetransition through either a Gibbs or Maxwell construction. These are followedby Bayesian parameter estimation of the associated gravitational-wave signalsusing the $\tt{NRPMw}$ waveform model, with priors inferred from the analysisof the inspiral signal. We assess the ability of the model to measure thepostmerger peak frequency $f_2^{\rm peak}$ and identify aspects that should beimproved in the model. We show that, even at postmerger signal to noise ratiosas low as 10, the model can distinguish (at the 90% level) $f_2^{\rm peak}$between binaries with and without a phase transition in most cases.Phase-transition induced deviations in the $f_2^{\rm peak}$ from thepredictions of equation-of-state insensitive relations can also be detected ifthey exceed $1.6\,\sigma$. Our results suggest that next-generationgravitational wave detectors can measure phase transition effects in binaryneutron star mergers. However, unless the phase transition is ``strong'',disentangling it from other hadronic physics uncertainties will requiresignificant theory improvements.

Detectability of QCD phase transitions in binary neutron star mergers: Bayesian inference with the next generation gravitational wave detectors