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arXiv · 1609.06306

The Parallel-Repeated Magic Square Game is Rigid

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

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Matthew Coudron, Anand Natarajan. 2016-09-20. The Parallel-Repeated Magic Square Game is Rigid. https://arxiv.org/abs/1609.06306

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