It has long been known that the existence of certain superquantum nonlocal correlations would cause communication complexity to collapse. The absurdity of a world in which any nonlocal binary function could be evaluated with a constant amount of communication in turn provides a tantalizing way to distinguish quantum mechanics from incorrect theories of physics; the statement "communication complexity is nontrivial" has even been conjectured to be a concise information-theoretic axiom for characterizing quantum mechanics. We directly address the viability of that perspective with two results. First, we exhibit a nonlocal game such that communication complexity collapses in any physical theory whose maximal winning probability exceeds the quantum value. Second, we consider the venerable CHSH game that initiated this line of inquiry. In that case, the quantum value is about 0.85 but it is known that a winning probability of approximately 0.91 would collapse communication complexity. We provide evidence that the 0.91 result is the best possible using a large class of proof strategies, suggesting that the communication complexity axiom is insufficient for characterizing CHSH correlations. Both results build on new insights about reliable classical computation. The first exploits our formalization of an equivalence between amplification and reliable computation, while the second follows from an upper bound on the threshold for reliable computation with formulas of noisy XOR and AND gates.

翻译：长久以来，人们已知某些超量子非局域关联会导致通信复杂度坍塌。若在只需恒定通信量即可评估任意非局域二元函数的世界中，这种荒谬性反而为区分量子力学与错误物理理论提供了诱人途径；甚至有人推测"通信复杂度是非平凡的"这一论断可作为刻画量子力学的简洁信息论公理。我们通过两个结果直接探讨该视角的可行性。首先，我们构造了一个非局域博弈：在任何最大获胜概率超过量子值的物理理论中，通信复杂度都会坍塌。其次，我们考察了开启该研究方向的经典CHSH博弈：其量子值约为0.85，但已知约0.91的获胜概率即可导致通信复杂度坍塌。我们通过大规模证明策略表明0.91这一结果是最优的，暗示通信复杂度公理不足以刻画CHSH关联。这两个结果均基于对经典可靠计算的新见解：第一个结果利用了我们对放大与可靠计算等价性的形式化表述，第二个结果则源于含噪异或门与与门公式的可靠计算阈值上界。