Quantum teleportation through noisy channels with multi-qubit GHZ states

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 equation 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 n is an element of {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 nGHZ state under most noisy channels. However, nGHZ state preserves same quantum information with respect to Einstein-Podolsky-Rosen and 3GHZ states where the noise is in x direction in which the fidelity remains unchanged. We explicitly show that Jung et al.'s conjecture (Phys Rev A 78:012312, 2008), namely "average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels," is not valid for 3GHZ and 4GHZ states.