• DOI:10.1103/PhysRevLett.128.080507
• Corpus ID: 236950798

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
        }
}

• S. A. Rather, Adam Burchardt, +3 authors K. Życzkowski
• 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 power among all bipartite unitary gates of this dimension, or a perfect tensor with four indices, each running from one to six. This special state deserves the appellation golden AME state, as the golden ratio appears prominently in its elements. This result allows us to construct a pure nonadditive quhex quantum error detection code ((3,6,2))_{6}, which saturates the Singleton bound and allows one to encode a six-level state into a triplet of such states.