重复幻方博弈是刚性的
The Parallel-Repeated Magic Square Game is Rigid
摘要：
我们表明，$n$轮平行重复的魔术广场游戏的Mermin和佩雷斯是刚性的，在这个意义上，任何纠缠策略成功的概率$1 -\varepsilon$，球员的共享状态是$O(\mathrm{poly}(n\varepsilon))$ -接近$2n$ EPR对下的局部等距。此外，我们还证明了，在局域等距下，当作用于共享态时，纠缠策略中的参与者的测量必须是$O(\mathrm{poly}(n\varepsilon))$接近“理想”策略。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
