  Composite quantum systems exhibit non-local correlations. These counter
intuitive correlations form a resource for quantum information processing and
quantum computation. In our previous work on two qubit maximally entangled
mixed states, we observed that entangled states, states that can be used for
quantum teleportaion, states that violate Bell-CHSH inequality and states that
do not admit local hidden variable description is the hierarchy in terms of the
order of nonlocal correlations. In order to establish this hierarchy, in the
present work, we investigate the effect of noise on two quibt states that
exhibit higher order nonlocal correlations. We find that dilapidation of
nonlocal correlations in the presence of noise follow the same hierarchy, that
is, higher order nonlocal correlation disappears for small strength of noise,
where as lower order nonlocal correlations survive strong noisy environment. We
show the results for decoherence due to amplitude damping channel on various
quantum states. However, we observe that same hierarchy is followed by states
undergoing decoherence due to phase damping as well as depolarizing channels.
