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Entanglement and Contextuality
Entanglement is something that we don't attribute to classical systems. But there's a very high bar that you can set, such that if you prove that some phenomenon meets this bar, then it is truly non classical. It's pretty difficult to prove that something is contextual, but it can be done. So i think of contextuality as, at least in some cases, the thing behind entanglement - and provide speed up to quanum competitors.