A locally testable code is an error-correcting code that admits very efficient probabilistic tests of membership. Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of Reed-Muller codes. The natural test for tensor codes, the axis-parallel line vs. point test, plays an essential role in constructions of probabilistically checkable proofs. We analyze the axis-parallel line vs. point test as a two-prover game and show that the test is sound against quantum provers sharing entanglement. Our result implies the quantum-soundness of the low individual degree test, which is an essential component of the MIP* = RE theorem. Our proof also generalizes to the infinite-dimensional commuting-operator model of quantum provers.

翻译：本地测试代码是一种允许非常高效的会籍概率测试的错误校正代码。 Tensor 代码提供了一套简单的组合式组合式组合式的本地测试代码结构,将Reed- Muller 代码组合为通用的本地测试代码。 高频代码的自然测试, 轴- 平行线对点测试, 在概率校验证据的构造中起着关键作用 。 我们将轴- 平行线对点测试分析成一种双倍的游戏, 并显示测试对量子验证器的串联性是健全的。 我们的结果意味着低单度测试的量度判断性, 这是 MIP * = RE 参数的基本组成部分 。 我们的证据还概括了量子验证器的无限分流模型 。