The logical set of Gaussian states under the stabilizer subsystem decomposition

Abstract:Universal quantum computation requires non-Gaussianity in continuous-variable systems and non-stabilizerness in discrete-variable systems. Yet, mapping a Gaussian state into the Gottesman-Kitaev-Preskill logical subspace can yield a logical qubit with non-stabilizer resources. To understand how the continuous-variable structure determines logical resources, we characterize the image of single-mode Gaussian states under the corresponding extraction channel, known as the stabilizer subsystem decomposition. Specifically, we derive series expressions for the logical Bloch vector and characterize the resulting reachable set, enabling an analytical treatment of the robustness of magic of the logical states. We then turn this geometric framework into a certification tool: by mapping a discrete-variable qubit witness to a continuous-variable squeezing witness, we obtain lower bounds on the squeezing of prepared states. We also show that ensembles of Gaussian states can violate both stabilizer and classical bounds. Violation of the stabilizer bound certifies the relational resource known as "set-magic," while violation of the classical bound enables the certification of cryptographic randomness at moderate squeezing.

arXiv:2609.26898 [quant-ph]

(or arXiv:2609.26898v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26898 Focus to learn more arXiv-issued DOI via DataCite

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