Motivated by the limitations of near-term quantum devices, we study nonlocal games in the high-noise regime, where the two players may share arbitrarily many copies of a noisy entangled state. In this regime, existing rigidity theorems are unable to certify any nontrivial quantum structure. We first characterize the maximal quantum winning probabilities of the CHSH game [Clauser et al. '69], the Magic Square game [Mermin '90], and their 2-out-of-n variants [Chao et al. '18] as explicit functions of the noise rate. These characterizations enable the construction of device-independent protocols for estimating the underlying noise level. Building on these results, we prove noise-robust rigidity theorems showing that these games certify one, two, and n pairs of anticommuting Pauli observables, respectively. To our knowledge, these are the first rigidity results of Pauli measurements that remain sound in the high-noise regime, which has applications in Measurement-Device-Independent (MDI) cryptography and studying the computational power of Multi-prover Interactive Proof System with entanglement and a vanishing completeness-soundness gap ($\text{MIP}^*_0$). Our proofs rely on Sum-of-Squares decompositions and Pauli analysis techniques originating from quantum proof systems and quantum learning theory, respectively.

翻译：受近期量子设备局限性的启发，我们研究了高噪声区域下的非局域博弈，其中两个玩家可以共享任意多份噪声纠缠态的副本。在此区域下，现有的刚性定理无法认证任何非平凡的量子结构。我们首先刻画了CHSH博弈[Clauser等人 '69]、Magic Square博弈[Mermin '90]及其2-out-of-n变体[Chao等人 '18]的最大量子获胜概率，并将其表示为噪声率的显式函数。这些刻画使得构建用于估计底层噪声水平的设备无关协议成为可能。在这些结果的基础上，我们证明了对噪声鲁棒的刚性定理，表明这些博弈分别认证了一对、两对和n对反交换泡利可观测量。据我们所知，这是首个在高噪声区域下仍然有效的泡利测量刚性结果，可应用于测量设备无关密码学，以及研究基于纠缠且具有消失的完备性-可靠性间隙的多证明者交互证明系统的计算能力（$\text{MIP}^*_0$）。我们的证明分别依赖于来源于量子证明系统和量子学习理论的平方和分解与泡利分析技术。