YQI Colloquium - Michel Janssen - University of Minnesota Twin Cities

Taking Mermin to Bananaworld: Mermin’s test of a Bell inequality in terms of Bub’s magic bananas.

Using the imagery of Jeffrey Bub’s 2016 book Bananaworld, I analyze a well-known experimental setup that David Mermin introduced in 1981 to convey to a general audience that quantum mechanics predicts correlations stronger than those allowed classically. Using correlation arrays, the workhorse of Bub’s Bananaworld, I derive a Bell inequality for this setup similar to the familiar Clauser-Horne-Shimony-Holt (CHSH) inequality. Using one key result from quantum mechanics, I use the same correlation arrays to derive the elliptope inequality, a non-linear inequality expressing the quantum bound on correlations in Mermin’s setup. Following statisticians Udny Yule (1896) and Ronald Fisher (1915), I show that this inequality is not specific to quantum mechanics but is a general constraint on the correlation between three random variables with zero expectation value. I use these results for plausibility arguments that these quantum correlations call for something like the Hilbert space formalism and that this formalism is first and foremost about generating and constraining probabilities.