Multiple measurements of quasars acting as standard probes: model
  independent calibration and exploring the Dark Energy Equation of States
  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.
