Workshop on "GeometrieS for Quantum Information"

socket L'objectif de ces rencontres est d'échanger différents regards sur de nouvelles approches géométriques de la théorie de l'information quantique. Plus précisémment la question de l'intrication des systèmes d'états purs, à travers l'étude des variétés homogènes pour un groupe de Lie, et celle des configurations d'opérateurs, à travers des problèmes de géométrie finie, seront abordées pendant cette journée.

The aim of this workshop is to exchange different perspectives on new geometric tools for quantum information. More precisely we will discuss the entanglement of pure multipartite systems, from the point of view of homogeneous varieties, and we will discuss the geometry of Pauli operators from the perspective of finite geometry.

Jeudi 25 Septembre 2014 UTBM Sévenans Salle Séminaire IRTES-M3M

  • 9:30-10:15 Frédéric Holweck: The geometry of entanglement and the E8 adjoint variety
  • Abstract: In this talk I'll recall a geometric description of the tripartite entanglement of three qubit systems by aim of the construction of secant and tangential varieties of the set of separable states. Then I'll show how the structure of this fundamental case as well as other well-known tripartite type systems is related to the adjoint variety of the Lie algebra E8. More precisely the E8 adjoint variety allows us to construct a nested sequence of homognenous varieties, each featuring a type of tripartite entanglement. This nested sequence of homogeneous varieties is well known from geometers and was intensively studied 15 years ago.
  • 10:15-11:00 coffee break, discussions
  • 11:00-11:45 Peter Levay: Entanglement in Fermionic Fock Space
  • Abstract: TBA.
  • 11:45-12:30 discussions
  • 12:30-14:00 lunch
  • 14:15-15:00 Metod Saniga: From real Cayley-Dickson Algebras, through Veldkamp Spaces and Binomial Configurations, to Combinatorial Grassmannians
  • Abstract:here
  • 15:00-15:30 discussions
  • 16:00-16:45 Alain Giorgetti: Hypermaps, groups and connected permutations
  • Abstract: This talk presents a taxonomy of families of hypermaps, their correspondence with (conjugacy classes) of subgroups of the cartographic group, and some correspondences with families of connected permutations. Grothendieck's dessins d'enfants are then identified in this dictionary. Their relation with finite geometries underlying quantum contextuality has been shown in the submitted paper ``Quantum contextual finite geometries from dessins d'enfants'' by Michel, Frédéric, Metod and I. Finally, the talk will present the current achievements and remaining issues in bounded exhaustive generation by increasing size of representatives of these objects, for experiments in Magma or other languages​​.
  • 16:45-17:15 cofee break, discussions
  • 17:15-18:00 Michel Planat: contextuality from dessins d'enfants
  • Quantum theory does not allow quantum observables (for an Hilbert space of dimension greater than 2) to represent a non contextual reality. This impossibility can by illustrated by specific finite geometries configurations which can be recovered from the formalism of Grothendieck's "dessins d'enfants". [see 1404.6986 , 1310.4267, 1306.0356 (quant-ph)].
  • 18:00-18:30 discussions