  We present ALMA band 8 observations of the [OIII] 88um line and the
underlying thermal infrared continuum emission in the z=6.08 quasar CFHQS
J2100-1715 and its dust-obscured starburst companion galaxy (projected
distance: ~60 kpc). Each galaxy hosts dust-obscured star formation at rates >
100 M_sun/yr, but only the quasar shows evidence for an accreting 10^9 M_sun
black hole. Therefore we can compare the properties of the interstellar medium
in distinct galactic environments in two physically associated objects, ~1 Gyr
after the Big Bang. Bright [OIII] 88um emission from ionized gas is detected in
both systems; the positions and line-widths are consistent with earlier [CII]
measurements, indicating that both lines trace the same gravitational potential
on galactic scales. The [OIII] 88um/FIR luminosity ratios in both sources fall
in the upper range observed in local luminous infrared galaxies of similar dust
temperature, although the ratio of the quasar is smaller than in the companion.
This suggests that gas ionization by the quasar (expected to lead to strong
optical [OIII] 5008A emission) does not dominantly determine the quasar's FIR
[OIII] 88um luminosity. Both the inferred number of photons needed for the
creation of O++ and the typical line ratios can be accounted for without
invoking extreme (top-heavy) stellar initial mass functions in the starbursts
of both sources.
