An Operational Classification and Quantification of Multipartite Entangled States

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Abstract
The understanding of multipartite entanglement is still an open field of research. Both its characterization and quantification are not completely satisfactory yet. In this paper we shed new light on this problem by formalizing and extending an operational multipartite entanglement measure introduced in T. R. Oliveira, G. Rigolin, and M. C. Oliveira, Phys. Rev. A 73, 010305(R) (2006), which is inspired by the global entanglement first presented in D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002). Contrary to global entanglement, the main feature of this new measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows for the construction of an operational multipartite entanglement measure which, along with other properties, is able to distinguish among different multipartite entanglement states which global entanglement failed to discriminate and is maximum at the critical point of the Ising chain in a transverse magnetic field.

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