Can every set of incompatible measurements lead to genuine multipartite steering?

TL;DR

This paper establishes that measurement incompatibility is necessary and sufficient for genuine multipartite steering in scenarios with a single uncharacterized party, extending bipartite results to multipartite quantum systems.

Contribution

It proves the equivalence of incompatibility and genuine multipartite steering in certain multipartite quantum scenarios, and introduces new methods for analyzing multipartite correlations.

Findings

Incompatibility is necessary and sufficient for genuine multipartite steering with one uncharacterized party.

Genuine multipartite steering can be obtained from incompatible measurements using GHZ and W states.

The equivalence does not hold when there are multiple uncharacterized parties.

Abstract

Measurement incompatibility and bipartite quantum steering are known to display a strong connection: a set of measurements is incompatible if and only if it can lead to bipartite steering. Despite such a close link between these concepts in bipartite scenarios, little is known in the multipartite setting, where notions of genuine multipartite correlations play major roles. In this work we prove that, as in the bipartite case, incompatibility is also necessary and sufficient for genuine multipartite steering in any multipartite scenario with a single uncharacterised party. Interestingly, genuine multipartite steering can be extracted from any set of incompatible measurements using states which are not SLOCC equivalent, such as GHZ and W states. In contrast, we prove that this result does not hold in scenarios with more than one uncharacterised party, by presenting a set of incompatible measurements that can never lead to genuine multipartite steering in these cases. In order to obtain our main results, we introduce methods tailored for multipartite correlations, paving the way to understanding the role of measurement incompatibility beyond bipartite scenarios.