Speaker: Fred Holweck, Université de Technologie de Belfort-Montbéliard

 

 

Title: Spin representation and Fermionic Fock space

 

Abstract: In Quantum information, it is standard to study the classification of pure n-qubit states under the SLOCC (Stochastic Local Operations with Classical Communication) group. Mathematically, this problem boils down to the study of orbits in $V=(\CC^2)^{\otimes n}$ under the semi-simple Lie group $G=SL_2(\CC)^{\times n}$. But what about other Lie groups G and their representations V ? In this talk, after introducing a geometric framework to study classification of $n$-qubits quantum states in the language of auxiliary varieties of the highest weight orbit of the SLOCC group, I'll explain how similar constructions could be used for bosonic and fermionic states. In particular, I will talk about the relation between the spin representation and quantum states described in Fermionic Fock space. This last identification was used by Luke Oeding and myself to provide a new invariant useful for quantum information.