Laboratoire de Physique Théorique
Toulouse - UMR 5152

The negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers can be entangled and construct two quantum orthogonal Latin squares of this size. In other words, we found an Absolutely Maximally Entangled state AME(4,6) for four subsystems with six levels each, equivalently a 2-unitary matrix U of size 36 which maximizes the entangling power among all bi-partite unitary gates of this dimension, or a perfect tensor Tijkℓ with four indices, each running from one to six, or pure non-additive quantum error correction code ((4, 1, 3))_6.

Reference : Thirty-six Entangled Officers of Euler : Quantum Solution to a Classically Impossible Problem