论文标题
量子魔术矩形：表征和应用于认证的随机性扩展
Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion
论文作者
论文摘要
我们研究了Mermin-Peres Magic Square游戏对任意矩形维度的概括。在展示了一些一般属性之后，这些矩形游戏以其量子策略的最佳胜利概率而完全表征。我们发现，对于$ m \ times n $ dimensions $ m，n \ geq 3 $，有量子策略可以确定地获胜，而对于尺寸，$ 1 \ times n $量子策略并不多于经典策略。尺寸的最终案例$ 2 \ times n $更丰富，我们给出的上限和下限都优于经典策略。最后，我们将发现应用于量子认证的随机性扩展，以找到所有魔术矩形游戏的噪声耐受性和速率。为此，我们使用先前的结果来获得游戏的获胜概率，并具有杰出的输入，设备给出了确定性的结果，并遵循对C. A. Miller和Y. Shi的分析[Siam J. Comput。 46，1304（2017）]。
We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for quantum strategies. We find that for $m \times n$ rectangular games of dimensions $m,n \geq 3$ there are quantum strategies that win with certainty, while for dimensions $1 \times n$ quantum strategies do not outperform classical strategies. The final case of dimensions $2 \times n$ is richer, and we give upper and lower bounds that both outperform the classical strategies. Finally, we apply our findings to quantum certified randomness expansion to find the noise tolerance and rates for all magic rectangle games. To do this, we use our previous results to obtain the winning probability of games with a distinguished input for which the devices give a deterministic outcome, and follow the analysis of C. A. Miller and Y. Shi [SIAM J. Comput. 46, 1304 (2017)].
