The Parallel-Repeated Magic Square Game is Rigid

We show that the n-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability 1 -, the players' shared state is O (poly (n) ) -close to 2n EPR pairs under a local isometry. Furthermore, we show that, under local isometry, the players' measurements in said entangled strategy must be O (poly (n) ) close to the "ideal" strategy when acting on the shared state.