Not yet reviewed by Pith; the record is open.

Recently, two classes of quasar samples were identified, which are promising as new cosmological probes extending to higher redshifts. The first sample uses the nonlinear relation between the ultraviolet and X-ray luminosities of quasars to derive luminosity distances, whereas the linear sizes of compact radio quasars in the second sample can serve as standardized rulers, providing angular-diameter distances. In this study, under the assumption of a flat universe, we refreshed the calibration of multiple measurements of high-redshift quasars (in the framework of a cosmological-model-independent method with the newest Hubble parameters data). Furthermore, we placed constraints on four models that characterize the cosmic equation of state ($w$). The obtained results show that: 1) the two quasar samples could provide promising complementary probes at much higher redshifts, whereas compact radio quasars perform better than ultraviolet and X-ray quasars at the current observational level; 2) strong degeneracy between the cosmic equation of state ($w$) and Hubble constant ($H_0$) is revealed, which highlights the importance of independent determination of $H_0$ from time-delay measurements of strongly lensed Quasars; 3)together with other standard ruler probes, such as baryon acoustic oscillation distance measurements, the combined QSO+BAO measurements are consistent with the standard $\Lambda$CDM model at a constant equation of state $w=-1$; 4) ranking the cosmological models, the polynomial parametrization gives a rather good fit among the four cosmic-equation-of-state models, whereas the Jassal-Bagla-Padmanabhan (JBP) parametrization is substantially penalized by the Akaike Information Criterion and Bayesian Information Criterion criterion.