Outline 1. The two-qubit Pauli graph P 4 and the generalized quadrangle W(2) 2: Pauli graph P 4 and the projective line over the two-by-two matrix ring over Z 2 2: The multiline geometry of qubit/qutrit system Conclusion Annex: The N-qudits and symplectic polar spaces Finite Geometries and Quantum Information Michel Planat † and Metod Saniga ‡ † Institut FEMTO-ST/LPMO, 32 Avenue de l’Observatoire, F-25044 Besan¸con, France (michel.planat@femto-st.fr) ‡ ASTRONOMICAL INSTITUTE of the SLOVAK Academy of SCIENCES, SK-05960 Tatransk´ a Lomnica, Slovak Republic (msaniga@astro.sk) GdR Information Quantique, Aspet (Pyr´ en´ ees), June 5-8, 2007 Michel Planat † and Metod Saniga ‡ Finite Geometries and Quantum Information