Observations of H2 spectra in the line-of-sight of distant quasars may reveal a variation of the proton-electron mass ratio mu=m_p/m_e at high redshift, typically for z>2. Currently four high-quality systems (Q0347-383, Q0405-443, Q0528-250 and J2123-005) have been analyzed returning a constraint Dmu/mu < 1 x 10^{-5}. We present data and a mu-variation analysis of another system, Q2348-011 at redshift z_{abs}=2.42, delivering dmu/mu = (-1.5 pm 1.6) x 10^{-5}. In addition to observational data the status of the laboratory measurements is reviewed. The future possibilities of deriving a competitive constraint on Dmu/mu from the known high-redshift H2 absorbers is investigated, resulting in the identification of a number of potentially useful systems for detecting mu-variation.
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