AI 中文总结
本文证明全次数线对点检验的量子可靠性，利用个体次数定理，通过随机坐标变换和均匀线切片处理高次结果，但可靠性界仍依赖维度m。
AI 中文摘要
我们利用Ji、Natarajan、Vidick、Wright和Yuen的个体次数可靠性定理，证明了全次数对角线对点检验的量子可靠性。随机坐标变换产生了全次数至多为$md$的射影多项式解码器。检验的均匀线切片限制了次数大于$d$的结果的权重，这些结果通过共同的重新标记被移除。这种归约并未产生与维度无关的可靠性界：个体次数定理的$\operatorname{poly}(m)$依赖性仍然存在，如arXiv:2009.12982第1.2节所讨论。
英文摘要
We prove quantum soundness of the total-degree diagonal line-vs-point test using the individual-degree soundness theorem of Ji, Natarajan, Vidick, Wright, and Yuen. A random change of coordinates yields projective polynomial decoders of total degree at most $md$. The uniform-line slice of the test bounds the weight of outcomes of degree greater than $d$, which are removed by a common relabeling. This reduction does not yield a dimension-independent soundness bound: the $\operatorname{poly}(m)$ dependence of the individual-degree theorem persists, as discussed in Section 1.2 of arXiv:2009.12982.
