Greenberger-Horne-Zeilinger versus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>states: Quantum teleportation through noisy channels

TLDR

The paper compares the robustness of GHZ and W states for two‑party quantum teleportation through noisy channels and investigates how average fidelity relates to entanglement in mixed‑state channels. The authors analytically solve a Lindblad master equation to model the noisy channels that render the quantum channels mixed. Robustness depends on the noise type: GHZ outperforms W for x‑type Lindblad operators, W outperforms GHZ for y‑type, GHZ dominates at large noise strength for z‑type while W is better at small strength, and both states preserve equal information in isotropic noise.

Abstract

Which state loses less quantum information between Greenberger-Horne-Zeilinger (GHZ) and $W$ states when they are prepared for two-party quantum teleportation through a noisy channel? We address this issue by solving analytically a master equation in the Lindblad form with introducing the noisy channels that cause the quantum channels to be mixed states. It is found that the answer to this question is dependent on the type of noisy channel. If, for example, the noisy channel is $({L}_{2,x},{L}_{3,x},{L}_{4,x})$ type, where the $L$'s denote the Lindblad operators, the GHZ state is always more robust than the $W$ state, i.e., the GHZ state preserves more quantum information. In, however, the $({L}_{2,y},{L}_{3,y},{L}_{4,y})$-type channel the situation becomes completely reversed. In the $({L}_{2,z},{L}_{3,z},{L}_{4,z})$-type channel, the $W$ state is more robust than the GHZ state when the noisy parameter $(\ensuremath{\kappa})$ is comparatively small while the GHZ state becomes more robust when $\ensuremath{\kappa}$ is large. In isotropic noisy channel we found that both states preserve an equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.