We perform a detailed investigation of moderate-to-high quality X-ray spectra of ten of the most luminous active galactic nuclei (AGNs) known at z>4 (up to z~6.28). This study includes five new XMM observations and five archived X-ray observations (four by XMM and one by Chandra). We find that the X-ray power-law photon indices of our sample, composed of eight radio-quiet sources and two that are moderately radio loud, are not significantly different from those of lower redshift AGNs. The upper limits obtained on intrinsic neutral hydrogen column densities, N_H<~10^{22}-10^{23} cm^{-2}, indicate that these AGNs are not significantly absorbed. A joint fit performed on our eight radio-quiet sources, with a total of ~7000 photons, constrains the mean photon index of z>4 radio-quiet AGNs to Gamma=1.97^{+0.06}_{-0.04}, with no detectable intrinsic dispersion from source to source. We also obtain a strong constraint on the mean intrinsic column density, N_H<~3x10^{21} cm^{-2}, showing that optically selected radio-quiet AGNs at z>4 are, on average, not more absorbed than their lower-redshift counterparts. All this suggests that the X-ray production mechanism and the central environment in radio-quiet AGNs have not significantly evolved over cosmic time. The mean equivalent width of a putative neutral narrow Fe Ka line is constrained to be <~190 eV, and similarly we place constraints on the mean Compton reflection component (R<~1.2). None of the AGNs varied on short (~1 hr) timescales, but on longer timescales (months-to-years) strong variability is observed in four of the sources. In particular, the X-ray flux of the z=5.41 radio-quiet AGN SDSS 0231-0728 dropped by a factor of ~4 over a rest-frame period of 73 d. This is the most extreme X-ray variation observed in a luminous z>4 radio-quiet AGN.
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