Nonlocal Games
I’ve been thinking for a while about nonlocal games and how to explain them, as most of the examples are a bit esoteric (like the Magic Square game). I wonder if there’s a better way to emphasize the game aspect in addition to the nonlocal one.
CSHS Game
In each of these you and another player are working together, you can strategize beforehand but cant communicate during the game (alternatively from a physics perspective this is about the speed of light and casuality, you’re casually independent systems)
The referee comes into the room and shows you a card with a number on it, you and your partner (separately) each choose your own numbers in response, if they add up to the ref’s target number you win
There are some obvious solutions to this, I could always pick 0 and my partner just chooses the number itself; or we could divide the number by a half and both respond the same way. In either case our perfect strategy is not a result of communication, but of a consistent correlation between our responses. However consider a strategy where we can’t have certainty beforehand
The referee comes in to your room, shows you the target number, and flips a coin. You win if the number you pick plus your partner’s number adds to the target, UNLESS both coins come up heads, then you only win if they do NOT add up to the target
This is essentially the CSHS game in disguise. Here the best we can do is to use the same strategy and just hope double heads doesn’t hit, however if my partner and I shared quantum entanglement we can do better. Although entanglement doesn’t allow for communication, it does allow for correlation, which is how the strategy works.
What I really want to figure out next are better ways to visualize the probability polytopes to show how supra-quantum correlations (violating the Tsirelson bound) change that shape.