We experimentally demonstrate the validity of non-equilibrium fluctuation
relations by using a quantum coherent conductor. In equilibrium the
fluctuation-dissipation relation leads to the correlation between current and
current noise at the conductor, namely, Johnson-Nyqusit relation. When the
conductor is voltage-biased so that the non-linear regime is entered, the
fluctuation theorem has predicted similar non-equilibrium fluctuation
relations, which hold true even when the Onsager-Casmir relations are broken in
magnetic fields. Our experiments qualitatively validate the predictions as the
first evidence of this theorem in the non-equilibrium quantum regime.
In the appendix, we give simple deduction of the higher order correlations
between the current and the current noise based on the fluctuation theorem.