This video shows the “CHSH Game”, a gamified version of Bell’s Theorem.

### Some History

- Bell’s Theorem is due to John Stuart Bell in 1964.
- The CHSH inequality, by John Clauser, Michael Horne, Abner Shimony, and Richard Holt, improved on it in 1969.
- The CHSH game by R. Cleve, P. Hoyer, B. Toner and J. Watrous in 2004. This opened a new research direction of combining interactive proofs with quantum entanglement, which ended up producing interesting results. See more about it in this video: https://youtu.be/2H8629BCbkM

### About "Bell Locality"

The formal statement of it is this requirement of the probability distribution:

P(x,y|a,b,particle1,particle2)=P(x|a,particle1)P(y|b,particle2)

This means that the outcomes are independent given the input bits and the respective particle statements.

Another way to say that is as stated in the video: that given the particle the top player has, we can specify the table P(x|a,particle1), and it makes no difference what happens with the bottom player (or the other way around of course).

Bell’s theorem proves this is not what’s happening.

As stated in the closing slide, this conclusion relies on a few more background assumptions:

- Each measurement has one outcome. According to the “many-worlds” theory a measurement can have multiple outcomes, and Bell locallity may still hold with this interpretation.
- The referee can choose random bits. According to “superdeterminisim” world view, there’s no such thing as randomness, and it might be that the referee chooses bits somehow pre-determined to match the particles held by the players.