Optimal detection of entanglement in Greenberger-Horne-Zeilinger states
Alastair Kay · Physical Review A · 2011
We present a broad class of $N$-qubit Greenberger-Horne-Zeilinger (GHZ)-diagonal states such that nonpositivity under the partial transpose operation is necessary and sufficient for the presence of entanglement, including many naturally arising instances such as dephased GHZ states. Furthermore, our proof directly leads to an entanglement witness which saturates this bound. The witness is applied to thermal GHZ states to prove that the entanglement can be extremely robust to system imperfections.