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

TL;DR

This paper investigates the intrinsic randomness in tripartite Bell experiments using the Mermin-Bell inequality, providing tight bounds on guessing probabilities and exploring implications for device-independent secret sharing.

Contribution

It offers the first tight bounds on guessing probabilities for three-party Mermin-Bell violations and discusses the feasibility of device-independent secret sharing based on this inequality.

Findings

Tight bounds on guessing probabilities as a function of Mermin violation.

Analysis suggests device-independent secret sharing with Mermin inequality is unlikely.

Provides analytical insights into tripartite nonlocality and randomness.

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.