Franz Luef: A time-frequency framework for GKP-codes: Part 1

Abstract: This is the first of two talks on time-frequency methods for GKP-codes, a well-studied class of quantum error-correcting codes. The focus will be on developing the theory of Gabor frames for symplectically integral lattices in phase space, as used in GKP codes, and present GKP-codes from this perspective. The duality theorem of Gabor analysis and the Zak transform are crucial in our approach, as well as the Banach-Gelfand triple based on the Feichtinger algebra and its continuous dual, the space of mild distributions. We will discuss that the space of mild distributions provides a convenient setting for ideal GKP-codes, and that there is a natural projection onto the space of ideal codes if we view use results about Heisenberg modules over noncommutative tori.This is based on joint work with Eduard Ortega (NTNU Trondheim), who is also going to give the second talk.