  We investigate the effect of quantum decoherence and relaxation in neutrino
oscillations using MINOS and T2K data. The formalism of open quantum systems is
used to describe the interaction of a neutrino system with the environment,
where the strength of the interaction is regulated by a decoherence parameter
$\Gamma$. We assume an energy dependence parameterized by $\Gamma = \gamma_0
(E/\mbox{GeV})^n$, with $n=-2,0,+2$, and consider three different scenarios,
allowing the investigation of the effect of relaxation and of constraining the
solar and atmospheric sectors to the same decoherence parameter. The MINOS and
T2K data present a complementary behavior, with regard to our theoretical
model, resulting in a better sensitivity for $n = +2$ and $n = -2$,
respectively. We perform a combined analyses of both experimental data, which
also include a reactor constraint on $\sin^2 \theta_{13}$, and observe an
independence of the results to the scenarios we investigate. As highlight of
our analyses we obtain the best limit on $\gamma_0$ for the energy dependence
of $n = -2$, reporting an upper bound of $1.7 \times 10^{-23}$~GeV, at the 90\%
confidence level.
