Quantum talk with Adam Mickiewicz

Speaker: Adam Burchardt from Adam Mickiewicz University Poznań.

Title: Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem

Abstract: 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. During the talk, I will briefly present the problem of multipartite entanglement, and its relation to classical and quantum combinatorial designs.