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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 possibly share an isomorphism of their symmetry algebras with those of rotations in corresponding dimensions 3, 6, 91. Such isomorphisms are valuable for use in quantum information. Simple algebraic analysis, however, already rules out the last case so that one and two qubits are the only instances of such isomorphism of the algebras and of a local homomorphism of the corresponding symmetry groups. A more mathematical topological analysis of the group spaces is also provided demonstrating their topological inequivalence. © 2013 World Scientific Publishing Company.

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International Journal of Quantum Information