The genuinely multipartite nonlocality of graph states is model-dependent

TL;DR

This paper examines different definitions of genuinely multipartite nonlocality (GMNL) in quantum states, showing that their applicability varies with the type of quantum state and communication model, highlighting the need for precise conceptual frameworks.

Contribution

It introduces and compares three definitions of GMNL, demonstrating their differences and implications for various quantum states like cluster and GHZ states.

Findings

Caterpillar graph states have LOSR-GMNL.

Cluster states lack LONC-GMNL, GHZ states possess it.

Different GMNL definitions impact quantum nonlocality benchmarking.

Abstract

Bell's theorem proves that some quantum state correlations can only be explained by bipartite non-classical resources. The notion of genuinely multipartite nonlocality (GMNL) was later introduced to conceptualize the fact that nonclassical resources involving more than two parties in a nontrivial way may be needed to account for some quantum correlations. In this letter, we first recall the contradictions inherent to the historical definition of GMNL. Second, we turn to one of its redefinitions, called Local-Operations-and-Shared-Randomness GMNL (LOSR-GMNL), proving that all caterpillar graph states (including cluster states) have this second property. Finally, we conceptualize a third, alternative definition, which we call Local-Operations-and-Neighbour-Communication GMNL (LONC-GMNL), that is adapted to situations in which short-range communication between some parties might occur. We show that cluster states do not have this third property, while GHZ states do. Beyond its technical content, our letter illustrates that rigorous conceptual work is needed before applying the concepts of genuinely multipartite nonlocality, genuine multipartite entanglement or entanglement depth to benchmark the nonclassicality of some experimentally-produced quantum system. We note that most experimental works still use witnesses based on the historical definitions of these notions, which fail to reject models based on bipartite resources.