We consider the collision model of Ziman et al. and study the robustness of $N$-qubit Greenberger-Horne-Zeilinger (GHZ), $W$, and linear cluster states. Our results show that $N$-qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of $W$ states could be more robust than that of linear cluster states. We indicate that the collision model of Ziman et al. could provide a physical mechanism for some known results in this area of investigation. More importantly, we show that it could give a clue as to how $N$-partite distillable entanglement would be relatively rare in our macroscopic classical world.

• Received 24 February 2006

DOI:https://doi.org/10.1103/PhysRevA.74.012307