can we imagine a set of instantaneous information-sharing rules that allow Alice and Bob to satisfy the rules all the time? Yes, Popescu and Rohrlich showed, we can. We can permit the boxes even more non-local exchange of information than is granted by quantum mechanics, still without violating relativity. These super-quantum boxes have become known as Popescu–Rohrlich (PR) boxes. Their improved performance comes from more efficient sharing of information. In general, communications are very inefficient because they involve exchanging lots of information that doesn’t feature in the final
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