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PreprintCC BY 4.0arXiv

Quantum entropy and the Bannai--Ito multiplicity conjecture

  • Gary Greaves
  • Haoran Zhu
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Abstract

We prove that the multiplicities of every symmetric Q-polynomial association scheme form a log-concave sequence. This resolves the 1984 unimodality conjecture of Bannai and Ito and establishes both related inequalities conjectured by Stanton. Our proof is a novel application of strong subadditivity and weak monotonicity inequalities for quantum entropy.

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Cite

BibTeXRIS
BibTeX
@misc{greaves2026quantum,
  title = {{Quantum entropy and the Bannai--Ito multiplicity conjecture}},
  author = {Gary Greaves and Haoran Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12573},
  eprint = {2609.12573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12573},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum entropy and the Bannai--Ito multiplicity conjecture
AU  - Gary Greaves
AU  - Haoran Zhu
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12573
UR  - https://arxiv.org/abs/2609.12573
AB  - We prove that the multiplicities of every symmetric Q-polynomial association scheme form a log-concave sequence. This resolves the 1984 unimodality conjecture of Bannai and Ito and establishes both related inequalities conjectured by Stanton. Our proof is a novel application of strong subadditivity and weak monotonicity inequalities for quantum entropy.
ER  -