On the geometry and invariants of qubits, quartits and octits

Michel Planat (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

Four level quantum systems, known as quartits, and their relation to two- qubit systems are investigated group theoretically. Following the spirit of Klein's lectures on the icosahedron and their relation to Hopf sphere bra- tions, invariants of complex re ection groups occuring in the theory of qubits and quartits are displayed. Then, real gates over octits leading to the Weyl group of E8 and its invariants are derived. Even multilevel systems are of interest in the context of solid state nuclear magnetic resonance.

Mots clés: Multilevel systems; quartits; nite groups; invariant theory.; invariant theory

Domaines: Physique Quantique [quant-ph]; Théorie des groupes [math.GR]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Michel Planat. On the geometry and invariants of qubits, quartits and octits. International Journal of Geometric Methods in Modern Physics, 2011, 8 (2), pp.303-313. ⟨hal-00482803v2⟩