Polytope structures for Greenberger-Horne-Zeilinger diagonal states
arXiv:2104.07871 · doi:10.1088/1751-8121/ac2c5a
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.
arXiv comment13 pages, to appear in Journal of Physics A: Mathematical and Theoretical
References in corpus (27)
- Quantum entanglement
- Entanglement detection
- On the volume of the set of mixed entangled states
- Robustness of entanglement
- Classification of mixed three-qubit states
- Separability of very noisy mixed states and implications for NMR quantum computing
- Taming multiparticle entanglement
- Separability criteria for genuine multiparticle entanglement
- Classification of multi-qubit mixed states: separability and distillability properties
- Largest separable balls around the maximally mixed bipartite quantum state
- Separability and distillability of multiparticle quantum systems
- Multi-Particle Entanglement Purification Protocols
- Quantum Discord and the Geometry of Bell-Diagonal States
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Hilbert--Schmidt volume of the set of mixed quantum states
- Separable balls around the maximally mixed multipartite quantum states
- Tensor products of convex sets and the volume of separable states on N qudits
- Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes
- The volume of separable states is super-doubly-exponentially small
- Separability criteria for several classes of -partite quantum states
- Qubit-Qutrit Separability-Probability Ratios
- Construction of multi-qubit optimal genuine entanglement witnesses
- Relative volume of separable bipartite states
- Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
- Separability criterion for three-qubit states with a four dimensional norm
- On the convex cones arising from classifications of partial entanglement in the three qubit system
- Convex bodies of states and maps