Trade-offs in multi-party Bell inequality violations in qubit networks

Abstract

Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.

15 pages, 5 figures

References in corpus (7)

• 14-qubit entanglement: creation and coherence
• Certified randomness in quantum physics
• Geometry of the set of quantum correlations
• Monogamy of Bell's inequality violations in non-signaling theories
• Higher entropic uncertainty relations for anti-commuting observables
• Monogamy of Bell correlations and Tsirelson's bound
• Measurement uncertainty from no-signaling and non-locality

Cited by in corpus (10)

• Geometry of the set of quantum correlations
• Shareability of Quantum Steering and its Relation with Entanglement
• Randomness versus nonlocality in the Mermin-Bell experiment with three parties
• Bell monogamy relations in arbitrary qubit networks
• Trade-off relations of l_1-norm coherence for multipartite systems
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
• Genuine monogamy relations in no-signaling theories - a geometric approach
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy