“…In the first part of our work, we describe the model and the Hamiltonian of our quantum system, and we must point out that, although this Hamiltonian will be time explicitly dependent, if we consider weak interaction between our system and the environment (the characteristic times of the quantum system are much longer than those of the environment) as a first approximation, the above mentioned Markovian-Lindblad master type equation can be still used for our study [11,17,18]. One needs to mention that even this linear chain of three nuclear spins model for solid state quantum computer has not been built yet, it has been very useful for theoretical studies about implementation of quantum gates and quantum algorithms [19][20][21] which can be extrapolated to other solid state quantum computers [22,23]. After doing this, we establish the five cases to be considered with the quantum-environment system: independent environment interaction (A), pure dephasing interaction (B), correlated dissipation interaction (C), dephasing correlated interaction (D), and thermalization case (E).…”