Dynamics of entanglement and quantum states transitions in spin-qutrit systems under classical dephasing and the relevance of the initial state

We provide a detailed analysis of the time-evolutions of free and bound entangled states in a two-qutrit system under the effects of local/non-local classical dephasing noises. Namely the Ornstein-Uhlenbeck (OU) and the static noise are considered. The importance of the initial state is also analyzed by considering two completely different initially entangled states and their respective locally equivalent states by means of local unitary operation (LUO). The qutrits isotropic and bound entangled states are studied and we analyze their dynamical evolution to infer quantum states transition in the system. We demonstrate the absence of state transitions for isotropic-like states, unlike bound entangled-like states where free entangled states may lose distillability. Disentanglement however occurs for independents environments no matter the initial state. Meanwhile, for a common environment we show that indefinite free entanglement survival can be achieved (suppression of distillability sudden death) by converting the initial state using the LUO, hence saving free entanglement in the bipartite high dimensional quantum system, useful for quantum information and processing purposes. (paper)