The classification of multipartite quantum correlation

Abstract

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.

13+4 pages, 3 figures. v3: small fix in fig.1, does not affect results

References in corpus (5)

• Multipartite entanglement in spin chains
• Partial separability and entanglement criteria for multiqubit quantum states
• Probability density function characterization of multipartite entanglement
• The correlation theory of the chemical bond
• Partial separability revisited: Necessary and sufficient criteria

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• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Detecting genuine multipartite entanglement via machine learning
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• Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
• Alternatives of entanglement depth and metrological entanglement criteria
• On the convex cones arising from classifications of partial entanglement in the three qubit system
• There exist infinitely many kinds of partial separability/entanglement
• The quantum marginal independence problem
• Criteria for partial entanglement of three qubit states arising from distributive rules