  In this manuscript, the behavior of the Wigner function of accelerated and
non-accelerated two qubit system passing through different noisy channels is
discussed. The decoherence of the initial quantum correlation due to the noisy
channels and the acceleration process is investigated by means of Wigner
function. The negative (positive) behavior of the Wigner function predicts the
gain of the quantum (classical) correlations. Based on the upper and lower
bounds of the Wigner function, the entangled initial state loses its quantum
correlation due the acceleration process and the strengths of the noisy
channels. However, by controlling the distribution angles, the decoherence of
these quantum correlation may be suppressed. For accelerated state, the
robustness of the quantum correlations contained in the initial state appears
in different ranges of the distribution angles depending on the noisy type. For
the bit phase flip and the phase flip channels, the robustness of the quantum
correlations is shown at any acceleration and large range of distribution
angles. However, the fragility of the quantum correlation is depicted for large
values for strength of the bit flip channel. Different profiles of the Wigner
function are exhibited for the quantum and classical correlations, cup, lune,
hemisphere.
