  A tight non-linear relation between the X-ray and the optical-ultraviolet
(UV) emission has been observed in Active Galactic Nuclei (AGN) over a wide
range of redshift and several orders of magnitude in luminosity, suggesting the
existence of an ubiquitous physical mechanism regulating the energy transfer
between the accretion disc and the X-ray emitting corona. Recently, our group
developed a method to use this relation in the observational cosmology, turning
quasars into standardizable candles. This work has the main aim to investigate
the potential evolution of this correction at high redshifts. We thus studied
the $L_{\rm X}-L_{\rm UV}$ relation for a sample of quasars in the redshift
range 4<$z$<7, adopting the selection criteria proposed in our previous work
regarding their spectral properties. The resulting sample consists of 53 Type 1
(unobscured) quasars, observed either with Chandra or XMM-Newton, for which we
performed a full spectral analysis, determining the rest-frame 2 keV flux
density, as well as more general X-ray properties such as the estimate of
photon index, and the soft (0.5-2 keV) and hard (2-10 keV) unabsorbed
luminosities. We find that the relation shows no evidence for evolution with
redshift. The intrinsic dispersion of the L$_X$-L$_{UV}$ for a sample free of
systematics/contaminants is of the order of 0.22 dex, which is consistent with
previous estimates from our group on quasars at lower redshift.
