Abstract
The conventional definition of nonlocality pertains solely to two subsystems, which falls short in fully describing the potential of quantum mechanics observed in multipartite systems. This role is better fulfilled by a variant of nonlocality called Genuine Multipartite NonLocality (GMNL). However, as researchers delved deeper into the concept of GMNL, an intriguing observation regarding its behaviour in certain scenarios came to light. It was discovered that it is possible to start with a measurement statistic that does not exhibit GMNL, and by grouping specific events together, end up with a GMNL measurement statistic. To this end, a new definition of GMNL based on the network scenario was introduced called LOSR-GMNL. In our work, we study this new definition with the aim of characterising the set of quantum states exhibiting LOSR-GMNL. We show that large classes of graph states for arbitrary, prime local dimension, as well as states that are sufficiently close to said states, are LOSR-GMNL.
