  X-ray observations provide a unique probe of the accretion disk corona of
supermassive black holes (SMBHs). In this paper, we present a uniform
\emph{Chandra} X-ray data analysis of a sample of 152 $z\geq4.5$ quasars. We
firmly detect 46 quasars of this sample in 0.5-2~keV above 3~$\sigma$ and
calculate the upper limits of the X-ray flux of the remaining. We also estimate
the power law photon index of the X-ray spectrum of 31 quasars. 24 of our
sample quasars are detected in the FIRST or NVSS radio surveys; all of them are
radio-loud. We statistically compare the X-ray properties of our $z\geq4.5$
quasars to other X-ray samples of AGN at different redshifts. The relation
between the rest-frame X-ray luminosity and other quasar parameters, such as
the bolometric luminosity, UV luminosity, or SMBH mass, show large scatters.
These large scatters can be attributed to the narrow luminosity range at the
highest redshift, the large measurement error based on relatively poor X-ray
data, and the inclusion of radio-loud quasars in the sample. The $L_{\rm
X}-L_{\rm UV}$ relationship is significantly sub-linear. We do not find a
significant redshift evolution of the $L_{\rm X}-L_{\rm UV}$ relation,
expressed either in the slope of this relation, or the departure of individual
AGNs from the best-fit $\alpha_{\rm OX}-L_{\rm UV}$ relation
($\Delta\alpha_{\rm OX}$). The median value of the X-ray photon index is
$\Gamma\approx1.79$, which does not show redshift evolution from $z=0$ to
$z\sim7$. The X-ray and UV properties of the most distant quasars could
potentially be used as a standard candle to constrain cosmological models. The
large scatter of our sample on the Hubble diagram highlights the importance of
future large unbiased deep X-ray and radio surveys in using quasars in
cosmological studies.
