发表机构
Stony Brook University（石溪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明经典低个体度测试在缺少对角线测试且无其他兼容机制时无法保持量子可靠性，并给出了在 (m,d)=(2,2) 且 q 为任意奇素数时需该测试的实例。
AI 中文摘要
为了证明经典低个体度测试的量子可靠性，\n\cite{JNVWY20LID} 的作者定义了三个子测试，即轴平行线测试、自洽性测试和对角线测试。一个有趣的问题是能否移除对角线测试。在本文中，我们表明，在没有其他兼容机制的情况下，不能简单地移除对角线测试。因此，在 MIP*=RE 的证明中，如 \cite{JNVWY20LID} 所述，将“条件线性函数”替换为“坐标删除函数”本身并不能保持所需的可靠性。\cite{JNVWY20LID} 的作者发现了一个在 (m, d, q) = (2, 2, 4) 时需要对角线测试的例子；我们给出了一个在 (m, d) = (2, 2) 且 q 为任意奇素数时需要对角线测试的例子。
英文摘要
To prove the quantum soundness of the classical low-individual-degree test, the authors of \cite{JNVWY20LID} defined three subtests, namely the axis-parallel lines test, the self-consistency test, and the diagonal-lines test. An interesting question is whether the diagonal-lines test can be removed. In this paper, we show that the diagonal-lines test cannot simply be removed without another compatibility mechanism. Consequently, replacing the "conditional linear functions" by "coordinate deletion functions" in the proof of MIP*=RE, as mentioned in \cite{JNVWY20LID}, does not by itself preserve the required soundness. The authors of \cite{JNVWY20LID} found an example that requires the diagonal-lines test when \((m, d, q) = (2, 2, 4)\); we give an example when \((m, d) = (2, 2)\) and \(q\) is any odd prime.
