On the validity of factorization law for the entanglement evolution of two qubits

The validity of factorization law for the entanglement evolution of two qubits coupled to two independent non-Markovian channels is investigated. It is found that for some initial states, such as the Bell state and the maximally entangled mixed state, the entanglement can be characterized by the factorized entanglement when the effects of the channels are weak. For the general initial states, the factorized entanglement provides us with a good approximation to characterize the entanglement dynamics when the entanglement is large.