Equation of motion for multiqubit entanglement in multiple independent noisy channels

Abstract

We investigate the possibility and conditions to factorize the entanglement evolution of a multiqubit system passing through multi-sided noisy channels. By means of a lower bound of concurrence (LBC) as an entanglement measure, we derive an explicit formula of the LBC evolution of the N-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) state under some typical noisy channels, based on which two kinds of factorizing conditions for the LBC evolution are presented. In this case, the time-dependent LBC can be determined by a product of initial LBC of the system and the LBC evolution of a maximally entangled GGHZ state under the same multi-sided noisy channels. We analyze the realistic situations where these two kinds of factorizing conditions can be satisfied. In addition, we also discuss the dependence of entanglement robustness on the number of qubits and that of the noisy channels.