Year: 2026
Type: preprint
Abstract: We develop a time--frequency framework for lattice GKP codes in which ideal codewords are realized in the modulation space $M^\infty$ and identified, through a vector-valued Zak transform, with a finite logical fibre over the continuous syndrome torus. Multi-window Gabor analysis then represents the logical vector by a finite block of adjoint-lattice coefficients. We prove that the normalized block map is an isometry, obtain an explicit recovering projection, and derive stable logical reconstruction. We further construct normalizable GKP approximants as lattice-envelope Gabor multipliers and establish weak-$*$ convergence and asymptotically isometric encoding. Finally, we recover displacement syndromes from phase relations between translated coefficient blocks and quantify their stability under additive perturbations.
Source: arXiv (Cornell University)
Authors: Luef, Franz, Ortega, Eduard
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212255034