This chapter discusses a Bananaworld version of a correlation analyzed by Einstein, Podolsky, and Rosen in a 1935 argument for the incompleteness of quantum mechanics. This correlation can be simulated by Alice and Bob with a shared random local resource, which is equivalent to showing that the correlation has a common cause explanation. A superquantum correlation proposed by Popescu and Rohrlich can’t be perfectly simulated with local resources, but a quantum simulation with entangled quantum states can do better than the optimal simulation with local resources (up to a quantum limit called the “Tsirelson bound”). So there is no common cause explanation of the correlation of a pair of Popescu–Rohrlich bananas. Since the correlated events can be arbitrarily far apart, there is no direct causal explanation either, because information would have to be transmitted faster than light between the correlated events. This is a version of Bell’s theorem.
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