Most games like the CHSH game require measuring Bell states in different bases depending on Alice and Bobs local bit strings. What if Alice and Bob only share Bell states and can only do local qubit flips (Pauli X) and computational basis measurements? Presumably you cant violate a Bell inequality - the only power they really have is to steer the others qubit to a 0 or a 1 which is guaranteed correlated or anti-correlated with theirs (the latter by applying the Pauli X). Are there any communication complexity type tasks where they can demonstrate an advantage over classical theory? (e.g. https://arxiv.org/pdf/1012.5043.pdf)



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