The Parallel-Repeated Magic Square Game is Rigid

Abstract

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 $1-\epsilon$, the players' shared state is $O(\mathrm{poly}(n\epsilon ))$-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 $O(\mathrm{poly}(n\epsilon ))$ close to the "ideal" strategy when acting on the shared state.

29 pages

References in corpus (2)

• Robust Self Testing of the Singlet
• Self-testing graph states