  We investigate entanglement properties of multipartite states under the
influence of decoherence. We show that the lifetime of (distillable)
entanglement for GHZ-type superposition states decreases with the size of the
system, while for a class of other states -namely all graph states with
constant degree- the lifetime is independent of the system size. We show that
these results are largely independent of the specific decoherence model and are
in particular valid for all models which deal with individual couplings of
particles to independent environments, described by some quantum optical master
equation of Lindblad form. For GHZ states, we derive analytic expressions for
the lifetime of distillable entanglement and determine when the state becomes
fully separable. For all graph states, we derive lower and upper bounds on the
lifetime of entanglement. To this aim, we establish a method to calculate the
spectrum of the partial transposition for all mixed states which are diagonal
in a graph state basis. We also consider entanglement between different groups
of particles and determine the corresponding lifetimes as well as the change of
the kind of entanglement with time. This enables us to investigate the behavior
of entanglement under re-scaling and in the limit of large (infinite) number of
particles. Finally we investigate the lifetime of encoded quantum superposition
states and show that one can define an effective time in the encoded system
which can be orders of magnitude smaller than the physical time. This provides
an alternative view on quantum error correction and examples of states whose
lifetime of entanglement (between groups of particles) in fact increases with
the size of the system.
