  Two recent discoveries have made it possible for us to begin using high-z
quasars as standard candles to construct a Hubble Diagram (HD) at z > 6. These
are (1) the recognition from reverberation mapping that a relationship exists
between the optical/UV luminosity and the distance of line-emitting gas from
the central ionizing source. Thus, together with a measurement of the velocity
of the line-emitting gas, e.g., via the width of BLR lines, such as Mg II, a
single observation can therefore in principle provide a determination of the
black hole's mass; and (2) the identification of quasar ULAS J1120+0641 at z =
7.085, which has significantly extended the redshift range of these sources,
providing essential leverage when fitting theoretical luminosity distances to
the data. In this paper, we use the observed fluxes and Mg II line-widths of
these sources to show that one may reasonably test the predicted high-z
distance versus redshift relationship, and we assemble a sample of 20 currently
available high-z quasars for this exercise. We find a good match between theory
and observations, suggesting that a more complete, high-quality survey may
indeed eventually produce an HD to complement the highly-detailed study already
underway (e.g., with Type Ia SNe, GRBs, and cosmic chronometers) at lower
redshifts. With the modest sample we have here, we show that the R_h=ct
Universe and LCDM both fit the data quite well, though the smaller number of
free parameters in the former produces a more favorable outcome when we
calculate likelihoods using the Akaike, Kullback, and Bayes Information
Criteria. These three statistical tools result in similar probabilities,
indicating that the R_h=ct Universe is more likely than LCDM to be correct, by
a ratio of about 85% to 15%.
