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

@article{Rather2021ThirtysixEO,
title={Thirty-six Entangled Officers of Euler: Quantum Solution to a Classically Impossible Problem.},
author={Suhail Ahmad Rather and Adam Burchardt and Wojciech T. Bruzda and Grzegorz Rajchel-Mieldzio'c and Arul Lakshminarayan and Karol Życzkowski},
journal={Physical review letters},
year={2021},
volume={128 8},
pages={
080507
}
}
• Published 11 April 2021
• Physics
• Physical review letters
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 are entangled, and construct orthogonal quantum Latin squares of this size. As a consequence, we find an example of the long-elusive Absolutely Maximally Entangled state AME(4,6) of four subsystems with six levels each, equivalently a 2-unitary matrix of size 36, which maximizes the entangling…
15 Citations

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