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The classification of multipartite quantum correlation

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arxiv 1806.04392 v3 pith:HPOHZKOL submitted 2018-06-12 quant-ph math-phmath.MP

The classification of multipartite quantum correlation

classification quant-ph math-phmath.MP
keywords classificationmultipartitecorrelationpropertiesstructureworkatomsboils
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In multipartite entanglement theory, the partial separability properties have an elegant, yet complicated structure, which boils down in the case when multipartite correlations are considered. In this work, we elaborate this, by giving necessary and sufficient conditions for the existence and uniqueness of the class of a given class-label, by the use of which we work out the structure of the classification for some important particular cases, namely, for the finest classification, for the classification based on k-partitionability and k-producibility, and for the classification based on the atoms of the correlation properties.

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