Randomness versus nonlocality in the Mermin-Bell experiment with three parties

Abstract

The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by quantum physics, quantified by the guessing probability, can generally be bounded numerically. However, currently only a few exact analytic solutions are known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell inequality. Here, we study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality. We give tight upper bounds on the guessing probabilities associated with one and two of the parties' measurement outcomes as a function of the Mermin inequality violation. Finally, we discuss the possibility of device-independent secret sharing based on the Mermin inequality and argue that the idea seems unlikely to work.

References in corpus (24)

• Quantum secret sharing
• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Bounding the set of quantum correlations
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• All multipartite Bell correlation inequalities for two dichotomic observables per site
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• More Randomness from the Same Data
• Using complete measurement statistics for optimal device-independent randomness evaluation
• Extremal correlations of the tripartite no-signaling polytope
• Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations
• Device-independent quantum key distribution secure against adversaries with no long-term quantum memory
• Device-Independent Randomness Generation in the Presence of Weak Cross-Talk
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• Trade-offs in multi-party Bell inequality violations in qubit networks

Cited by in corpus (14)

• Device-Independent Secret Sharing and a Stronger Form of Bell Nonlocality
• Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
• Device-independent tests of structures of measurement incompatibility
• Entropy bounds for multiparty device-independent cryptography
• Statistical testing of random number generators and their improvement using randomness extraction
• Boosting device-independent cryptography with tripartite nonlocality
• Practical randomness amplification and privatisation with implementations on quantum computers
• Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Minimum Detection Efficiencies for Loophole-free Genuine Nonlocality Tests
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Device-independent Shannon entropy certification
• Tight analytic bound on the trade-off between device-independent randomness and nonlocality