Michael Walter, Brent Doran, David Gross, Matthias Christandl
Multi-particle entanglement is a fundamental feature of quantum mechanics and an essential resource for quantum information processing and interferometry. Yet, our understanding of its structure is still in its infancy. A systematic classification of multiparticle entanglement is provided by the study of equivalence of entangled states under stochastic local operations and classical communication. Determining the precise entanglement class of a state in the laboratory, however, is impractical as it requires measuring a number of parameters exponential in the particle number. Here, we present a solution to the challenge of classifying multi-particle entanglement in a way that is both experimentally feasible and systematic, i.e., applicable to arbitrary quantum systems. This is achieved by associating to each class an entanglement polytope--the collection of eigenvalues of the one-body reduced density matrices of all states contained in the class. Determining whether the eigenvalues of an entangled state belong to a given entanglement polytope provides a new criterion for multiparticle entanglement. It is decidable from a linear number of locally accessible parameters and robust to experimental noise. We describe an algorithm for computing entanglement polytopes for any number of particles, both distinguishable and indistinguishable. Further, we illustrate the power of entanglement polytopes for witnessing genuine multipartite entanglement and relate them to entanglement distillation. The polytopes for experimentally relevant systems comprised of either several qubits or bosonic two-level systems are explained.
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http://arxiv.org/abs/1208.0365
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