1212.2378 (Yaroslav Pavlyukh et al.)

1, 2, and 6 qubits, and the Ramanujan-Nagell theorem    [PDF]

Yaroslav Pavlyukh, A. R. P. Rau

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.

View original: http://arxiv.org/abs/1212.2378