We revisit neutrino oscillations in matter considering the open quantum system framework which allows to introduce possible decoherence effects generated by New Physics in a phenomenological manner. We assume that the decoherence parameters $gamma_{ij}$ may depend on the neutrino energy, as $gamma_{ij}=gamma_{ij}^{0}(E/text{GeV})^n$ $(n = 0,pm1,pm2) $. The case of non-uniform matter is studied in detail, both within the adiabatic approximation and in the more general non-adiabatic case. In particular, we develop a consistent formalism to study the non-adiabatic case dividing the matter profile into an arbitrary number of layers of constant densities. This formalism is then applied to explore the sensitivity of IceCube and DeepCore to this type of effects. Our study is the first atmospheric neutrino analysis where a consistent treatment of the matter effects in the three-neutrino case is performed in presence of decoherence. We show that matter effects are indeed extremely relevant in this context. We find that IceCube is able to considerably improve over current bounds in the solar sector ($gamma_{21}$) and in the atmospheric sector ($gamma_{31}$ and $gamma_{32}$) for $n=0,1,2$ and, in particular, by several orders of magnitude (between 3 and 9) for the $n=1,2$ cases. For $n=0$ we find $gamma_{32},gamma_{31}< 4.0cdot10^{-24} (1.3cdot10^{-24})$ GeV and $gamma_{21}<1.3cdot10^{-24} (4.1cdot10^{-24})$ GeV, for normal (inverted) mass ordering.
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