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 $\operatorname{poly}(m)$ dependence of the individual-degree theorem persists, as discussed in Section 1.2 of arXiv:2009.12982.

Quantum Physics (quant-ph); Computational Complexity (cs.CC)

arXiv:2609.27129 [quant-ph]

(or arXiv:2609.27129v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.27129 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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