Nonlocal games are a framework in quantum information theory which provide a mathematical basis for testing entanglement between particles. Beginning several decades ago with the work on the CHSH game for which the 2022 Nobel Prize in Physics was awarded, experimental implementations of nonlocal games have produced a large body of evidence for the empirical existence of quantum entanglement. In this talk, we will describe a method to recast the formalism of nonlocal games from the standard language of projection-valued measures on Hilbert spaces into a more concrete ‘statistical’ set-up that involves averaging random variables on finite sets. In particular, we will present a result of the speaker asserting these formulations are equivalent in the sense that they produce the same families of possible measurements. We will also discuss how to interpret the recent MIP* = RE incomputability theorem in this statistical context.
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