1, 2, and 6 qubits, and the Ramanujan-Nagell theorem
  A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding dimensions $3, 6, 91$. Topological analysis, however, rules out the last possibility. 
Yaroslav Pavlyukh, A. R. P. Rau
math-ph math.MP quant-ph