Optimal Detection of Entanglement in GHZ States

TL;DR

This paper introduces a class of N-qubit GHZ-diagonal states for which non-positivity under partial transpose is both necessary and sufficient for entanglement detection, providing a practical entanglement witness applicable to thermal states.

Contribution

It identifies a broad class of GHZ-diagonal states with a complete entanglement criterion and derives an optimal entanglement witness for these states.

Findings

Non-positivity under partial transpose is necessary and sufficient for entanglement in the class.

The entanglement witness saturates the bound and is effective for thermal GHZ states.

Entanglement in thermal GHZ states is highly robust to imperfections.

Abstract

We present a broad class of states which are diagonal in the basis of N-qubit GHZ states such that non-positivity under the partial transpose operation is necessary and sufficient for the presence of entanglement. This class includes many naturally arising instances such as dephased or depolarised 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.