Dynamical evolution of entanglement of a three-qubit system driven by a classical environmental colored noise

The effects of \( 1/f^{\alpha } (\alpha =1,2)\) noise stemming from one or a collection of random bistable fluctuators (RBFs), on the evolution of entanglement, of three non-interacting qubits are investigated. Three different initial configurations of the qubits are analyzed in detail: the Greenberger–Horne–Zeilinger (GHZ)-type states, W-type states and mixed states composed of a GHZ state and a W state (GHZ-W). For each initial configuration, the evolution of entanglement is investigated for three different qubit–environment (Q-E) coupling setups, namely independent environments, mixed environments and common environment coupling. With the help of tripartite negativity and suitable entanglement witnesses, we show that the evolution of entanglement is extremely influenced not only by the initial configuration of the qubits, the spectrum of the environment and the Q-E coupling setup considered, but also by the number of RBF modeling the environment. Indeed, we find that the decay of entanglement is accelerated when the number of fluctuators modeling the environment is increased. Furthermore, we find that entanglement can survive indefinitely to the detrimental effects of noise even for increasingly larger numbers of RBFs. On the other hand, we find that the proficiency of the tripartite entanglement witnesses to detect entanglement is weaker than that of the tripartite negativity and that the symmetry of the initial states is broken when the qubits are coupled to the noise in mixed environments. Finally, we find that the 1 / f noise is more harmful to the survival of entanglement than the \( 1/f^{2} \) noise and that the mixed GHZ-W states followed by the GHZ-type states preserve better entanglement than the W-type ones.