A *nonlocal game* is a way to interpret any [[Bell Inequality|Bell inequality]]. Instead of thinking about correlations in a quantum experiment, we can think about a game played by two players where they are trying to collaboratively get the maximum score. Here, we describe the nonlocal game/Bell game for a specific Bell inequality.
In the game, two players, [[Alice and Bob]], get two random inputs and have to give an output to a referee. The inputs are binary, i.e. $0$ and $1$. Depending on the input, they can independently decide for a binary output, also $0$ and $1$. Their goal is to get the highest score given the following rule:
- Both inputs are $1$: Alice and Bob get a point if they answer the same.
- All other inputs: Alice and Bob get a point if their answers are different.
Importantly, Alice and Bob are allowed to communicate before the game to fix a strategy, but not during the game.
![[bell_game.excalidraw.light.svg]]
One can show that the maximal success probability for any given round with a classical strategy is 75%. One such strategy is that Alice and Bob always answer $1$, Independent of the input.
If Alice and Bob used a quantum strategy, i.e. they share entanglement, then they can win the same game with 87% probability. Here, quantum mechanics provides a genuine advantage.
>[!read]- Further Reading
> - [[Bell Nonlocality]]
> - [[Quantum Advantage]]
>[!ref]- References
>- J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics Physique Fizika **1**, 195 (1964).physics