Adam Burchardt (Jagiellonian University): Thirty-six entangled officers of Euler

Chaos and quantum chaos seminar at the Institute of Physics, Jagiellonian University.

A quantum analogon of the famous problem of 36 officers of Euler is presented. Although it is well known that the classical problem has no solutions, we found an explicit analytic solution of the quantum version of this problem, in which officers are allowed to be entangled. This unexpected result provides constructive solutions to the related problem of the existence of absolutely maximally entangled state AME(4,6) of four subsystems with six levels each. The existence of such a state is equivalent to the existence of a 2-unitary matrix of size 36, or a perfect tensor with four indices, each running from one to six, or a pure quantum error correction code ((4,1,3))6. Our result sheds some light on how to construct non-additive quantum error correction codes when the stabilizer approach fails.