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.

arXiv commentFinal version, 6 pages + appendix

References in corpus (42)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Bell nonlocality
• Violation of Bell's inequality under strict Einstein locality conditions
• Significant-loophole-free test of Bell's theorem with entangled photons
• Random Numbers Certified by Bell's Theorem
• A strong loophole-free test of local realism
• No Signalling and Quantum Key Distribution
• Non-locality and Communication Complexity
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• Bell's theorem for general N-qubit states
• Self-testing of quantum systems: a review
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Experimental entanglement of a six-photon symmetric Dicke state
• Permutationally invariant quantum tomography
• Quantum Communication between N partners and Bell's inequalities
• Maximally Non-Local and Monogamous Quantum Correlations
• Detecting non-locality in multipartite quantum systems with two-body correlation functions
• Monogamy of nonlocal quantum correlations
• Symmetries of the Bell correlation inequalities
• Cosmic Bell Test using Random Measurement Settings from High-Redshift Quasars
• Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements
• Four Photon Entanglement from Down Conversion
• Experimental observation of four-photon entanglement from down-conversion
• Spectral decomposition of Bell's operators for qubits
• Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
• Experimental violation of a cluster state Bell inequality
• Monogamy of Bell's inequality violations in non-signaling theories
• Correlation complementarity yields Bell monogamy relations
• Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations
• Limitations on sharing Bell nonlocality between sequential pairs of observers
• Elemental and tight monogamy relations in nonsignalling theories
• Genuine Multipartite Entanglement without Multipartite Correlations
• Bell inequality with an arbitrary number of settings and its applications
• Classification and monogamy of three-qubit biseparable Bell correlations
• Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
• Sharing nonlocality in quantum network by unbounded sequential observers
• Genuine $N$-partite entanglement without $N$-partite correlation functions
• Bell monogamy relations in arbitrary qubit networks
• Trade-offs in multi-party Bell inequality violations in qubit networks
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Simple and tight monogamy relations for a class of Bell inequalities

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• 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?