Robustness of multiqubit entanglement against local decoherence

Abstract

We investigate the disentanglement dynamics of generalized multiqubit Greenberger-Horne-Zeilinger-type states $\ensuremath{\mid}{\ensuremath{\Psi}}_{n,N}⟩=\ensuremath{\alpha}{\ensuremath{\mid}1⟩}^{\ensuremath{\bigotimes}n}{\ensuremath{\mid}0⟩}^{\ensuremath{\bigotimes}(N\ensuremath{-}n)}+\ensuremath{\beta}{\ensuremath{\mid}0⟩}^{\ensuremath{\bigotimes}n}{\ensuremath{\mid}1⟩}^{\ensuremath{\bigotimes}(N\ensuremath{-}n)}$ (with $1\ensuremath{\leqslant}n<N$) in a local decoherence environment. By adopting the time after which all the bipartite entanglements vanish or become negligibly small as the criterion of entanglement robustness, we show that states $\ensuremath{\mid}{\ensuremath{\Psi}}_{n,N}⟩$ are more robust than states $\ensuremath{\mid}{\ensuremath{\Psi}}_{N}⟩=\ensuremath{\alpha}{\ensuremath{\mid}0⟩}^{\ensuremath{\bigotimes}N}+\ensuremath{\beta}{\ensuremath{\mid}1⟩}^{\ensuremath{\bigotimes}N}$ in all respects. Since the two states $\ensuremath{\mid}{\ensuremath{\Psi}}_{N}⟩$ and $\ensuremath{\mid}{\ensuremath{\Psi}}_{n,N}⟩$ can be transformed into each other by local operations, we confirm that entanglement robustness can be enhanced by local operations though the amount of entanglement cannot.