  We present a study of the relation between X-rays and ultraviolet emission in
quasars for a sample of broad-line, radio-quiet objects obtained from the
cross-match of the Sloan Digital Sky Survey DR14 with the latest Chandra Source
Catalog 2.0 (2,332 quasars) and the Chandra COSMOS Legacy survey (273 quasars).
The non-linear relation between the ultraviolet (at 2500 A, $L_{O}$) and the
X-ray (at 2 keV, $L_{X}$) emission in quasars has been proved to be
characterised by a smaller intrinsic dispersion than the observed one, as long
as a homogeneous selection, aimed at preventing the inclusion of contaminants
in the sample, is fulfilled. By leveraging on the low background of Chandra, we
performed a complete spectral analysis of all the data available for the
SDSS-CSC2.0 quasar sample (i.e. 3,430 X-ray observations), with the main goal
of reducing the uncertainties on the source properties (e.g. flux, spectral
slope). We analysed whether any evolution of the $L_{X}-L_{O}$ relation exists
by dividing the sample in narrow redshift intervals across the redshift range
spanned by our sample, $z \simeq 0.5-4$. We find that the slope of the relation
does not evolve with redshift and it is consistent with the literature value of
$0.6$ over the explored redshift range, implying that the mechanism underlying
the coupling of the accretion disc and hot corona is the same at the different
cosmic epochs. We also find that the dispersion decreases when examining the
highest redshifts, where only pointed observations are available. These results
further confirm that quasars are `standardisable candles', that is we can
reliably measure cosmological distances at high redshifts where very few
cosmological probes are available.
