I am interested in quantum combinatorial games.
According to the Wikipedia page on the Sprague-Grundy theorem:
Every impartial game under the normal play convention is equivalent to a nimber
An impartial game is one in which at any given point in the game, each player is allowed exactly the same set of moves
Based on my understanding at this point, the CHSH game is an impartial game (Alice & Bob can both make the same sets of measurements).
I am curious how to realize both nim sums (which are equivalent to XOR, which correlates to CNOT) & nim multiplication for the analysis of quantum XOR games such as CHSH.