# 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…

## 15 Citations

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### 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers

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. The famous combinatorial problem of Euler concerns an arrangement of 36 oﬃcers from six diﬀerent regiments in a 6 × 6 square array. Each regiment consists of six oﬃcers each belonging to one of six…

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