Thirty-six quantum officers are entangled
Quantum Physics
2026-03-04 v1 Combinatorics
Abstract
There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers does not have a solution. However, it has a "quantum solution": there exist so-called entangled quantum Latin squares of order six [Rather et al., 2022]. We prove that mutually orthogonal quantum Latin squares of order six do not exist if entanglement is not allowed.
Cite
@article{arxiv.2603.02334,
title = {Thirty-six quantum officers are entangled},
author = {Simeon Ball and Robin Simoens},
journal= {arXiv preprint arXiv:2603.02334},
year = {2026}
}