We study the dynamics of four-qubit W state under various noisy environments by solving analytically the master equation in the Lindblad form in which the Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Als
o, we investigate the dynamics of the entanglement using the lower bound to the concurrence. It is found that while the entanglement decreases monotonically for Pauli-Z noise, it decays suddenly for other three noises. Moreover, by studying the time evolution of entanglement of various maximally entangled four-qubit states, we indicate that the four-qubit W state is more robust under same-axis Pauli channels. Furthermore, three-qubit W state preserves more entanglement with respect to the four-qubit W state, except for the Pauli-Z noise.
We study quantum correlation of Greenberger-Horne-Zeilinger (GHZ) and W states under various noisy channels using measurement-induced disturbance approach and its optimized version. Although these inequivalent maximal entangled states represent the s
ame quantum correlation in the absence of noise, it is shown that the W state is more robust than the GHZ state through most noisy channels. Also, using measurement-induced disturbance measure, we obtain the analytical relations for the time evolution of quantum correlations in terms of the noisy parameter $kappa$ and remove its overestimating quantum correlations upon implementing the ameliorated measurement-induced disturbance.
We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equat
ion with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for $n$-qubit GHZ states $nin{4,5,6}$ where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity we show that 3GHZ state is more robust than $n$GHZ state under most noisy channels. However, $n$GHZ state preserves same quantum information with respect to EPR and 3GHZ states where the noise is in $x$ direction in which the fidelity remains unchanged. We explicitly show that Jung ${it et, al.}$ conjecture [Phys. Rev. A ${bf 78}$, 012312 (2008)], namely, average fidelity with same-axis noisy channels are in general larger than average fidelity with different-axis noisy channels is not valid for 3GHZ and 4GHZ states.
