We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of GHZ and W states, for various environments.PACS numbers: 03.67.Mn,03.65.Yz,03.65.Ud The notion of entangled states is, since the early days of quantum mechanics, a key concept when it comes to distinguish between the quantum and the classical world. Besides this fundamental aspect, entanglement attracts considerable interest since it can be viewed as an indispensable ingredient for quantum information processing. Numerous experiments have recently been carried out in this area, in particular on the controlled generation of entanglement between many quantum systems [1,2,3,4,5] -such as to accomplish fundamental scalability requirements for quantum computation.An obstacle for the production and observation of multipartite entanglement resides in its fragility under the unavoidable interaction with the environment. This challenges the experimentalist, but also demands a proper theoretical description of multipartite entanglement in open systems. Despite recent progress in the understanding of decoherence processes in quantum systems, a systematic characterization of the environment induced loss of many-particle quantum correlations is still lacking, and this is specifically due to the difficulties in quantifying multipartite entanglement.Even for bipartite mixed states, apart from the particular case of two level systems where an exact solution is known [6], the situation is far from being simple. Some of the widely used indicators of entanglement, such as the positive partial transpose and negativity [7], fail to detect certain entangled states, while some other entanglement measures for mixed states require a high dimensional optimization procedure which only provides an upper bound, unable to reliably distinguish entangled from separable states. Only recently [8], a lower bound (together with a numerically manageable upper bound) for the concurrence of mixed bipartite quantum states was derived. In the multipartite case, one usually has to deal with bipartite cuts, where the N individual constituents are partitioned into two (arbitrarily chosen) subgroups. The available entanglement measures for bipartite systems thus become applicable, though different cuts or partitions may lead to different values of entanglement and, furthermore, the number of possible bipartite cuts increases rapidly with N .To improve on this situation, we will here scrutinize the effects of decoherence on multipartite entanglement measured by a suitable generalization of concurrencesensitive to multipartite correlations. Moreover, since different experimental strategies to produce multipartite entanglement are subject to different sources of decoherence, we implement our approach for different types of environment coupling, acting on different types of initially maximally entangled multipartite quantum states. This finally provides a versatile toolbox ...

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi-and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.

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We present a proposal for protecting states against decoherence, based on the engineering of pointer states. We apply this procedure to the vibrational motion of a trapped ion, and show how to protect qubits, squeezed states, approximate phase eigenstates, and superpositions of coherent states.