On the geometry and invariants of qubits, quartits and octits

Details On the geometry and invariants of qubits, quartits and octits On the geometry and invariants of qubits, quartits and octits

2010-05-12

arxiv.org/abs/1005.1997v2

International Journal of Geometric Methods in Modern Physics 8, 2 (2011) 303-313

Physics

Quantum Physics

version to be published in International Journal of Geometric Methods in Modern Physics (IJGMMP)

Scientific paper

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.

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