I'm trying to understand the strategy being put forward by the wikipedia article on quantum pseudo-telepathy to win the Mermin-Peres magic square game. It's frustrating, because I do understand how pseudo-telepathy works, I just can't make heads or tails of the grid in the article: I get that if I multiply the matrices in each cell across any row or column that I'll end up with +- identity matrix. I just don't know what that MEANS. I don't understand what the players are actually DOING that is represented by multiplying those matrices. I look at it and all I see are questions: - Where are the entangled qubits being fed into the system? - If Alice gets row 1, is she computing InputSuperposition * (X tensor I) * (X tensor X) * (I tensor X) on it? What is she computing? - How does she use the result to determine her moves? - The X, Y, and Z Pauli matrices never mix their results, so how is this computation relying on quantum mechanics at all? It seems like I could do it all classically, which is clearly wrong because there's no classical winning strategy. - Am I even right in assuming that the circle-with-X-inside is a tensor product, i.e. <1,2> tensor <3,4> = <3,6,4,8>? Any help would be appreciated. I've asked in multiple places but mostly gotten silence in response.