One feature of quantum correlations is that one can do computations beyond the best classical approach. It is also the core idea behind Bell's theorem, which reflects directly on the CHSH game.
In the CHSH game, a referee (Charlie) sends two random binary numbers (x and y) to Alice and Bob, while they should report two binary numbers (a and b). The winning cases happen if
x∧y=a⊻b
. Alice and Bob cannot communicate during the game, but they can decide on a strategy before hand. They can use a Bell state (i.e., an entangled quantum state) and by conditioning their local operations on that state, the results they report can go beyond the best classical strategy.
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QuantumCircuitOperator["CHSH"]"Diagram",
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One can generate the multivariate probability distribution of quantum measurements as follows:
