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
        }
}
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… 

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