Multiple Qubits as Symplectic Polar Spaces of Order Two

Metod Saniga (1) , Michel R. P. Planat (2)

1 Astronomical Institute of the Slovak Academy of Sciences
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

It is surmised that the algebra of the Pauli operators on the Hilbert space of N-qubits is embodied in the geometry of the symplectic polar space of rank N and order two, W_{2N - 1}(2). The operators (discarding the identity) answer to the points of W_{2N - 1}(2), their partitionings into maximally commuting subsets correspond to spreads of the space, a maximally commuting subset has its representative in a maximal totally isotropic subspace of W_{2N - 1}(2) and, finally, "commuting" translates into "collinear" (or "perpendicular").

Mots clés: Symplectic Polar Spaces of Order Two -- N-Qubits

Domaines: Physique Quantique [quant-ph]; Physique mathématique [math-ph]

Metod Saniga, Michel R. P. Planat. Multiple Qubits as Symplectic Polar Spaces of Order Two. Advanced Studies in Theoretical Physics, 2007, 1, pp.1 - 4. ⟨hal-00121565⟩