Polytope structures for Greenberger-Horne-Zeilinger diagonal states

Abstract

We explore the polytope structures for genuine entanglement, biseparability, full biseparability and Bell inequality of multi-qubit GHZ diagonal states. We first show that biseparable GHZ diagonal states make hypersimplices inside the simplices consisting of all GHZ diagonal states. Next, we consider full biseparability which is equivalent to positive partial transpose for GHZ diagonal states, and show that they make the convex hulls of simplices and cubes. We also visualize which part of the simplex violates multipartite Bell inequality. Finally, we compute precise volumes for genuine entanglement, biseparability, full biseparability and states violating Bell inequality among all GHZ diagonal states.

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

References in corpus (5)

• Entanglement detection
• Taming multiparticle entanglement
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• The volume of separable states is super-doubly-exponentially small
• Separability criteria for several classes of $n$-partite quantum states

Cited by in corpus (2)

• Alternatives of entanglement depth and metrological entanglement criteria
• There exist infinitely many kinds of partial separability/entanglement