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arXiv · 2603.02334

Thirty-six quantum officers are entangled

Simeon Ball·Robin Simoens
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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.

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Simeon Ball, Robin Simoens. 2026-03-02. Thirty-six quantum officers are entangled. https://arxiv.org/abs/2603.02334

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