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PreprintCC BY 4.0arXiv

The Low-Individual-Degree Test Without the Diagonal-Lines Test Is Not Quantum-Sound

  • Honghao Fu
  • Nengkun Yu
  • Tianrun Zhao
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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.

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Cite

BibTeXRIS
BibTeX
@misc{fu2026lowindividualdegree,
  title = {{The Low-Individual-Degree Test Without the Diagonal-Lines Test Is Not Quantum-Sound}},
  author = {Honghao Fu and Nengkun Yu and Tianrun Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.12346},
  eprint = {2609.12346},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12346},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Low-Individual-Degree Test Without the Diagonal-Lines Test Is Not Quantum-Sound
AU  - Honghao Fu
AU  - Nengkun Yu
AU  - Tianrun Zhao
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.12346
UR  - https://arxiv.org/abs/2609.12346
AB  - 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.
ER  -