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arXiv · 2412.17909

Continuous-variable designs and design-based shadow tomography from random lattices

Jonathan Conrad·Joseph T. Iosue·Ansgar G. Burchards·Victor V. Albert
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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.

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Jonathan Conrad, Joseph T. Iosue, Ansgar G. Burchards, Victor V. Albert. 2025-07-07. Continuous-variable designs and design-based shadow tomography from random lattices. https://doi.org/10.1103/dy4m-gq5c

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