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.
Highlights
Quantum theory predicts correlations incompatible with any local deterministic model [1, 2]
We study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality
The detection of nonlocal correlations in a Bell experiment implies at least some randomness in the measurement outcomes, regardless of the exact physical mechanism by which the correlations are produced, provided that communication between the sites is prohibited
Summary
Quantum theory predicts correlations incompatible with any local deterministic model [1, 2]. The simplest measure of randomness and typically the easiest to bound is the guessing probability This is defined as the probability that an additional observer, who may have partial access to the underlying quantum state, can correctly anticipate a given meas-. Beyond the CHSH scenario, guessing-probability bounds have been determined for violations of bipartite and multipartite chained Bell inequalities [19, 20]; Accepted in Quantum 2018-08-02, click title to verify these are derived assuming only the nosignalling constraints and they are not generally tight assuming the scenario is restricted to correlations and attacks allowed by quantum physics. The guessing probability Pg(A1|E) associated with the measurement outcome at one site, in terms of two independent Mermin expectation values. The guessing probability Pg(A1B1|E) associated with measurement outcomes at two sites, for a given violation of one Mermin inequality.
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