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.
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BibTeX
@misc{zamora2026logical,
title = {{The logical set of Gaussian states under the stabilizer subsystem decomposition}},
author = {Santiago Zamora and Kaustav Chatterjee and Ulrik Lund Andersen and Thiago Lucena de Macedo Guedes and Jonatan Bohr Brask and A. de Oliveira Junior and Rafael Chaves},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26898},
eprint = {2609.26898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26898},
}
RIS
TY - UNPB
TI - The logical set of Gaussian states under the stabilizer subsystem decomposition
AU - Santiago Zamora
AU - Kaustav Chatterjee
AU - Ulrik Lund Andersen
AU - Thiago Lucena de Macedo Guedes
AU - Jonatan Bohr Brask
AU - A. de Oliveira Junior
AU - Rafael Chaves
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26898
UR - https://arxiv.org/abs/2609.26898
AB - 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.
ER -