Can we distinguish quark stars from neutron stars with measurements of global properties?

The phase state of the dense stellar matter is an exciting topic in the area of nuclear astrophysics. It may be probed by observed properties of neutron stars from, for example, the currently operating satellites (NICER, Neutron star Interior Composition Explorer) and the gravitational-wave laser interferometers (Advanced LIGO, Virgo, and KAGRA). Based on our recent constrained parameter spaces of the equation of states of neutron stars and quark stars from LIGO/Virgo and NICER, we discuss the important role of an even-accurate determination of the stellar radius for distinguishing possible quark stars from neutron stars and our understanding of the QCD phase transition at finite density.