Continuous-variable designs and design-based shadow tomography from random lattices
arXiv:2412.17909 · doi:10.1103/dy4m-gq5c
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.
5+31 pages, 3 figures, comments welcome! v2 and v3 contain corrections of minor errors and further clarifications
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