We address some theoretical issues of the quantum decoherence phenomenon within the neutrino oscillation framework and carry out various tests the under DUNE simulated experimental environment. On the theoretical side, we provide a general expression for an invariant decoherence matrix under a quantum basis rotation. On the simulated experimental side, considering a rotation-invariant and noninvariant decoherence matrix, we study the impact on the fitting of the standard oscillation parameters, the sensitivity in the mass hierarchy, and the CP violation, combining the neutrino and antineutrino mode and all available neutrino oscillation probabilities channels. Furthermore, a sensitivity for the decoherence parameter of the order 10-24 GeV at 3σ is obtained for our best case. We also note that a degeneracy between the decoherence parameter and the CP violation phase remains, even though our analysis includes neutrino/antineutrino mode and all probabilities channels.