Two new non-equivalent three-qubit CHSH games

In this paper, we generalize to three players the well-known CHSH quantum game. To do so, we consider all possible 3 variables Boolean functions and search among them which ones correspond to a game scenario with a quantum advantage (for a given entangled state). In particular we provide two new three players quantum games where, in one case, the best quantum strategy is obtained when the players share a $GHZ$ state, while in the other one the players have a better advantage when they use a $W$ state as their quantum resource. To illustrate our findings we implement our game scenarios on an online quantum computer and prove experimentally the advantage of the corresponding quantum resource for each game.