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

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-v4 contain corrections of minor errors and further clarifications

Quantum Physics (quant-ph); Information Theory (cs.IT); Operator Algebras (math.OA)

arXiv:2412.17909 [quant-ph]

(or arXiv:2412.17909v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2412.17909 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1103/dy4m-gq5c Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.