Continuous-Variable Designs and Design-Based Shadow Tomography from Random Lattices
Jonathan Conrad, Joseph T. Iosue, Ansgar G. Burchards, Victor V. Albert · Physical Review Letters · 2025
We investigate state designs for continuous-variable quantum systems using the aid of latticelike quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that the set of all GKP states forms a rigged continuous-variable state 2-design for an n-mode system. 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.