PreprintCC BY 4.0arXiv
Quantum Soundness of a Total-Degree Line-versus-Point Test
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 poly(m) dependence of the individual-degree theorem persists, as discussed in Section 1.2 of arXiv:2009.12982.
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BibTeX
@misc{fu2026quantum,
title = {{Quantum Soundness of a Total-Degree Line-versus-Point Test}},
author = {Honghao Fu and Nengkun Yu and Tianrun Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.27129},
eprint = {2609.27129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27129},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Soundness of a Total-Degree Line-versus-Point Test
AU - Honghao Fu
AU - Nengkun Yu
AU - Tianrun Zhao
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.27129
UR - https://arxiv.org/abs/2609.27129
AB - 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 poly(m) dependence of the individual-degree theorem persists, as discussed in Section 1.2 of arXiv:2009.12982.
ER -