Factorization law of entanglement evolution between three qubits in non-Markovian environments

The entanglement evolution of a mixed three-qubit W-type state in three independent non-Markovian reservoirs with Lorentzian spectral density is investigated. The effects of the non-Markovianity of environment, initial state and the detuning on the entanglement dynamics in three-qubit system are presented. The results show that the entanglement between qubits in many-body system is more complicated than that in two-body system. First, the disentanglement criterion for two qubits is not suitable for multi qubits. Second, in many-body system, the effects of weight number characterizing the initial state distribution on the entanglement between two arbitrary qubits may be opposite. Further numerical calculations show that increasing the amount of non-Markovianity λ/γ, the purity of the initial quantum state or the detuning are all conducive to maintain the entanglement between qubits.