On the convex cones arising from classifications of partial entanglement in the three qubit system

Abstract

In order to classify partial entanglement of multi-partite states, it is natural to consider the convex hulls, intersections and differences of basic convex cones obtained from partially separable states with respect to partitions of systems. In this paper, we consider convex cones consisting of X-shaped three qubit states arising in this way. The class of X-shaped states includes important classes like Greenberger-Horne-Zeilinger diagonal states. We find all the extreme rays of those convex cones to exhibit corresponding partially separable states. We also give characterizations for those cones which give rise to necessary criteria in terms of diagonal and anti-diagonal entries for general three qubit states.

arXiv comment23 pages, to appear in Journal of Physics A: Mathematical and Theoretical

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Cited by in corpus (3)

• Alternatives of entanglement depth and metrological entanglement criteria
• There exist infinitely many kinds of partial separability/entanglement
• Polytope structures for Greenberger-Horne-Zeilinger diagonal states