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We study the dynamics of four-qubit W state under various noisy environmentsby solving analytically the master equation in the Lindblad form in which theLindblad operators correspond to the Pauli matrices and describe thedecoherence of states. Also, we investigate the dynamics of the entanglementusing the lower bound to the concurrence. It is found that while theentanglement decreases monotonically for Pauli-Z noise, it decays suddenly forother three noises. Moreover, by studying the time evolution of entanglement ofvarious maximally entangled four-qubit states, we indicate that the four-qubitW state is more robust under same-axis Pauli channels. Furthermore, three-qubitW state preserves more entanglement with respect to the four-qubit W state,except for the Pauli-Z noise.

The lower bound to the concurrence for four-qubit W state under noisy channels