Uncovering Non-Gaussianity through Multi-Copy Symmetries

• URL: http://arxiv.org/abs/2608.03755v1
• Date: Tue, 04 Aug 2026 14:44:22 GMT
• Title: Uncovering Non-Gaussianity through Multi-Copy Symmetries
• Abstract summary: We develop a group-theoretic multicopy approach to detect nonGaussianity.<n> Fixing the reference parameter purity, violationn identities certifies non-Gaussianity.<n>We show that relevant multi-copy detection can be estimated from bounded phase observables.
• Score: 10.018030428478928
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian states are fundamental in continuous-variable quantum information, yet characterizing non-Gaussianity remains challenging due to the non-convexity of the Gaussian set. Existing witnesses typically rely on Wigner negativity or other information-theoretic quantities. In this work, we develop a group-theoretic, multi-copy approach to detect non-Gaussianity in bosonic systems. We study passive linear optical transformations that mix copies of a quantum state and analyze their commutation with identical Gaussian unitaries applied to each copy. Orthogonal copy-mixing transformations commute with the symplectic part of the Gaussian action, while the displacement part restricts the symmetry to the stabilizer of the collective mode. This structure yields a family of witnesses satisfied by all single-mode Gaussian states. Fixing the thermal reference parameter via the purity, violation of these identities certifies non-Gaussianity. We illustrate the method with several single-mode examples and present an experimental protocol based on passive interferometry and photon-number-resolved detection, showing that the relevant multi-copy expectation values can be estimated from bounded phase observables. Finally, we extend the construction to multi-mode systems and discuss how the same symmetry framework may lead to quantitative measures of non-Gaussianity.

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