Large sets of mutually orthogonal quantum Latin squares

Simeon Ball, Robin Simoens

arXiv:2607.12933v2 Primary: math.CO Secondary: quant-ph

Abstract

How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classical sets of MOQLS of orders that are prime powers, improving both the previously known lower and upper bounds.

Disclosure

“nd Universities grant PID2023-147202NB-I00. Robin Simoens is supported by the Research Founda- tion Flanders (FWO) through the grant 11PG724N. We thank Eline Herdies and Leo Storme for helpful discussions towards proving Theorem 5. We used GPT-5.5 Pro by OpenAI to proofread the manuscript. References [1] A. S. Árnadóttir and D. E. Roberson. Group Invariant Quantum Latin Squares, 2025. arXiv:2501.00196. [2] S. Ball and R. Simoens. Thirty-six quantum officers are”
PDF page 7

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T18:53:10.913660Z

Structural counts

Pages 8 pdf

Theorems 6 source

Lemmas 5 source

Propositions 0 source

Corollaries 1 source

Definitions 1 source

Displayed equations 21 source

Bibliography entries 43 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file large_sets_of_MOQLS.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.