Unmasking the Polygamous Nature of Quantum Nonlocality

Abstract

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signalling principle and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of $(N-1)$ observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.

Final version, 6 pages + appendix

References in corpus (8)

• Experimental entanglement of a six-photon symmetric Dicke state
• Permutationally invariant quantum tomography
• Monogamy of Bell's inequality violations in non-signaling theories
• Genuine Multipartite Entanglement without Multipartite Correlations
• Classification and monogamy of three-qubit biseparable Bell correlations
• Sharing nonlocality in quantum network by unbounded sequential observers
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Simple and tight monogamy relations for a class of Bell inequalities

Cited by in corpus (6)

• The future of secure communications: device independence in quantum key distribution
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Nonlocality of Quantum States can be Transitive
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?