Genuine multipartite entanglement detection and lower bound of multipartite concurrence

TL;DR

This paper introduces a method to detect and classify genuine multipartite entanglement using a lower bound of multipartite concurrence, linking it to bipartite concurrences for practical operational detection.

Contribution

It provides a new criterion based on multipartite concurrence thresholds for entanglement detection and offers an effective way to classify genuine multipartite entanglement.

Findings

Derived a threshold for genuine multipartite entanglement detection.

Established a lower bound of multipartite concurrence via bipartite concurrences.

Analyzed tripartite systems as practical examples.

Abstract

The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglement. Then, we present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify the genuine multipartite entanglement. As applications, the genuine multipartite entanglement of tripartite systems is analyzed in detail.