Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Fu, Honghao, Yu, Nengkun, Zhao, Tianrun
Institution: Stony Brook University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212924349