Necessary and sufficient condition for Greenberger-Horne-Zeilinger diagonal states to be full $N$-partite entangled

TL;DR

This paper establishes a precise criterion for when GHZ-diagonal states are fully entangled across all qubits, linking full entanglement to the negativity of partial transposes in multiqubit systems.

Contribution

It provides a necessary and sufficient condition for full N-partite entanglement in GHZ-diagonal states based on partial transpose positivity.

Findings

Full N-partite entanglement corresponds to non-positivity of partial transposes.

The criterion applies specifically to GHZ-diagonal states.

The result simplifies entanglement detection in multiqubit systems.

Abstract

Recently, [{arXiv:0810.3134}] is accepted and published. We show that any $N$-qubit state which is diagonal in the Greenberger-Horne-Zeilinger basis is full $N$-qubit entangled state if and only if no partial transpose of the multiqubit state is positive with respect to any partition.