Thirty-six officers, artisanally entangled

Understand

A perfect tensor of order $d$ is a state of four $d$-level systems that is maximally entangled under any bipartition.

• These objects have attracted considerable attention in quantum information and many-body theory.
• Perfect tensors generalize the combinatorial notion of orthogonal Latin squares (OLS).
• Deciding whether OLS of a given order exist has historically been a difficult problem.