2022.12.13.
The Clauser-Horne-Shimony-Holt game is the simplest scenario in which the use of nonlocal no-signaling resources can be understood. In fact it is a game that is behind the classic Clauser-Horne-Shimony-Holt (CHSH) inequality that is famous for having a quantum violation. The game is also mentioned on the Wikipedia page of the celebrated inequality, and in many other works.
In the following we introduce the game, which is a very simple one. Then we illustrate, using our no-signaling box emulator, how a no-signaling resource can help the players to play the game with a higher reward, while still not being able to communicate. We will use a Popescu-Rorhlich (PR) box, which is a supra-quantum no-signaling resource, that is, it cannot be implemented physically. Nevertheless, as it is no-signaling, we can emulate it, and its behavior is easier to understand than the Bell-CHSH quantum experiment; it is possible even without any knowledge about quantum mechanics.