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We measure the broadband optical gain and absorption spectra between 0.1 and 0.7 eV in a two-phonon resonance design quantum cascade laser, with the infrared beam of a synchrotron light source, and correlate them to established simulation models, based on the density matrix formalism, and on the non-equilibrium Green's function theory. We show that accounting for the distribution of carriers in momentum space improves the description of the high-energy absorption from the excited states located close to the active wells and results in an accurate prediction of the gain.