Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

Abstract

We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.

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

References in corpus (6)

• Entanglement detection
• Entanglement criteria and full separability of multi-qubit quantum states
• Optimal Detection of Entanglement in GHZ States
• Construction of multi-qubit optimal genuine entanglement witnesses
• Three-qubit entanglement witnesses with the full spanning properties
• Various notions of positivity for bi-linear maps and applications to tri-partite entanglement

Cited by in corpus (3)

• The role of phases in detecting three-qubit entanglement
• Alternatives of entanglement depth and metrological entanglement criteria
• Polytope structures for Greenberger-Horne-Zeilinger diagonal states