The Projective Line Over the Finite Quotient Ring GF(2)[x]/hx3 − xi and Quantum Entanglement I. Theoretical Background Metod Saniga, Michel Planat To cite this version: Metod Saniga, Michel Planat. The Projective Line Over the Finite Quotient Ring GF(2)[x]/hx3 − xi and Quantum Entanglement I. Theoretical Background. 2006. hal-00020182v1 HAL Id: hal-00020182 https://hal.archives-ouvertes.fr/hal-00020182v1 Preprint submitted on 7 Mar 2006 (v1), last revised 6 Jun 2006 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Projective Line Over the Finite Quotient Ring GF(2)[x]/hx3 − xi and Quantum Entanglement I. Theoretical Background Metod Saniga† and Michel Planat‡ †Astronomical Institute, Slovak Academy of Sciences SK-05960 Tatransk´aLomnica, Slovak Republic (
[email protected]) and ‡Institut FEMTO-ST, CNRS, D´epartement LPMO, 32 Avenue de l’Observatoire F-25044 Besan¸con, France (
[email protected]) Abstract 3 The paper deals with the projective line over the finite factor ring R♣ ≡ GF(2)[x]/hx −xi. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As R♣ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap.