Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames

Abstract

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

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Cited by in corpus (8)

• Characterizing multipartite entanglement with moments of random correlations
• Quantum entanglement from random measurements
• Multipartite Entanglement Analysis From Random Correlations
• Analysing quantum systems with randomised measurements
• Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads
• Bell inequality violations with random mutually unbiased bases
• Quantum Key Distribution with no Shared Reference Frame
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?