  When subjected to a classical fluctuating field characterized by a Gaussian
process, we examine the {purity} and coherence protection in a three-level
quantum system. This symmetry of the three-level system is examined when the
local random field is investigated further in the noiseless and noisy regimes.
In~particular, we consider fractional Gaussian, Gaussian, Ornstein--Uhlenbeck,
and~power law noisy regimes. We show that the destructive nature of the
Ornstein--Uhlenbeck noise toward the symmetry of the qutrit to preserve encoded
{purity and coherence} remains large. Our findings suggest that properly
adjusting the noisy parameters to specifically provided values can facilitate
optimal extended {purity and coherence} survival. Non-vanishing terms appear in
the final density matrix of the single qutrit system, indicating that it is in
a strong coherence regime. Because~of all of the Gaussian noises, monotonic
decay with no revivals has been observed in the single qutrit system. In~terms
of coherence and information preservation, we find that the current qutrit
system outperforms systems with multiple qubits or qutrits using purity and von
Neumann entropy. A~comparison of noisy and noiseless situations shows that the
fluctuating nature of the local random fields is ultimately lost when
influenced using the classical Gaussian noises
