Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Fu, Honghao, Yu, Nengkun, Zhao, Tianrun
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214186350