A Quantum Combinatorial Design for the Euler Problem

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

We construct a solution to a quantum version of the famous combinatorial problem of euler which is based on a partition of 36 officers into nine groups of four elements each with four elements.The corresponding quantum states are locally equivalent to maximally entangled two-qubit states, hence each officer is entangled with at most three out of his colleagues.The entire quantum combinatorial design involves bell bases in nine complementary subspaces.