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Multipartite nonlocality is of great fundamental interest and constitutes auseful resource for many quantum information protocols. However, demonstratingit in practice, by violating a Bell inequality, can be difficult. Inparticular, standard experimental setups require the alignment of distantparties' reference frames, which can be challenging or impossible in practice.In this work we study the violation of certain Bell inequalities, namely theMermin, Mermin-Klyshko and Svetlichny inequalities, without shared referenceframes, when parties share a Greenberger-Horne-Zeilinger (GHZ) state.Furthermore, we analyse how these violations demonstrate genuine multipartitefeatures of entanglement and nonlocality. For 3, 4 and 5 parties, we show thatit is possible to violate these inequalities with high probability, when theparties choose their measurements from the three Pauli operators, defined onlywith respect to their local frames. Moreover, the probability of violation, andthe amount of violation, are increased when each party chooses theirmeasurements from the four operators describing the vertices of a tetrahedron.We also consider how many randomly chosen measurement directions are needed toviolate the Bell inequalities with high probability. We see that the obtainedlevels of violation are sufficient to also demonstrate genuine multipartiteentanglement and nonseparability. Finally, we show analytically that choosingfrom two measurement settings per party is sufficient to demonstrate themaximum degree of genuine multipartite entanglement and nonseparability withcertainty when the parties' reference frames are aligned in one direction sothat they differ only in rotations around one axis.

Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames