A quantitative witness for Greenberger-Horne-Zeilinger entanglement

TL;DR

This paper introduces an analytical method for efficiently quantifying GHZ-type entanglement in three-qubit states, linking entanglement detection and measurement, with potential for extension to larger systems.

Contribution

It presents a novel, simple analytical approach for quantifying multipartite entanglement, bridging detection and measurement, and generalizable beyond three qubits.

Findings

Provides a procedure for quantifying GHZ-type entanglement in three-qubit states.

Establishes a link between entanglement quantification and detection by witnesses.

Can be extended to higher dimensions and more than three parties.

Abstract

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger--type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result [Phys. Rev. Lett. 80, 2245 (1998)]. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.