Continuous-variable designs and design-based shadow tomography from random lattices
Quantum Physics
2026-01-14 v3 Information Theory
math.IT
Operator Algebras
Abstract
We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states forms a rigged continuous-variable state 2-design. We use these lattice state designs to construct a continuous variable shadow tomography protocol, derive sample complexity bounds for both global- and local GKP shadows under reasonable physical assumptions, and provide the physical gadgets needed to implement this protocol.
Keywords
Cite
@article{arxiv.2412.17909,
title = {Continuous-variable designs and design-based shadow tomography from random lattices},
author = {Jonathan Conrad and Joseph T. Iosue and Ansgar G. Burchards and Victor V. Albert},
journal= {arXiv preprint arXiv:2412.17909},
year = {2026}
}
Comments
5+31 pages, 3 figures, comments welcome! v2 and v3 contain corrections of minor errors and further clarifications