Stability of Macroscopic Entanglement under Decoherence

We investigate the lifetime of macroscopic entanglement under the influence of decoherence. For Greenberger-Horne-Zeilinger–type superposition states, we find that the lifetime decreases with the size of the system (i.e., the number of independent degrees of freedom), and the effective number of subsystems that remain entangled decreases with time. For a class of other states (e.g., cluster states), however, we show that the lifetime of entanglement is independent of the size of the system.

Figure 1

(a) GHZ states, 1D and 2D cluster states. (b) Upper bound on lifetime $\kappa \tau$ of $M$-party entanglement for GHZ states in systems with $N\to \infty$ particles for different $M$. (c) Same as (b) but with double-logarithmic axis. Note that the same figures are obtained for the lifetime of $N$-particle entanglement in $N$-particle systems (see text).