User:Boris Tsirelson/Sandbox1

Classical physics obeys the counterfactual definiteness and therefore negates entanglement. Classical apparata A, B cannot help Alice and Bob to always win (that is, agree on the intersection). What about quantum apparata? The answer is quite unexpected.

First, quantum apparata cannot ensure that Alice and Bob win always. Moreover, the winning probability does not exceed

${\frac {2+{\sqrt {2}}}{4}}=0.853\dots$

no matter which quantum apparata are used.

Second,