Measuring non-Gaussianity with Correlation

• URL: http://arxiv.org/abs/2508.19890v1
• Date: Wed, 27 Aug 2025 13:50:42 GMT
• Title: Measuring non-Gaussianity with Correlation
• Authors: Oliver Hahn, Ryuji Takagi,
• Abstract summary: Quantum non-Gaussianity is a key resource for quantum advantage in continuous-variable systems.<n>We introduce a general framework to quantify non-Gaussianity based on correlation generation.<n>We propose a sample-efficient experimental protocol to estimate non-Gaussianity using standard optical components.
• Score: 0.835541405153204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum non-Gaussianity is a key resource for quantum advantage in continuous-variable systems. We introduce a general framework to quantify non-Gaussianity based on correlation generation: two copies of a state become correlated at a $50{:}50$ beam splitter if and only if the state is non-Gaussian, with correlations reducing to entanglement in the pure-state case. This connection enables operational measures of non-Gaussianity, defined through correlation quantifiers such as R\'enyi-$\alpha$ entropy for pure states and R\'enyi-$\alpha$ mutual information for mixed states. We prove that all such measures are monotonic under Gaussian channels. Building on this framework, we propose a sample-efficient experimental protocol to estimate non-Gaussianity using standard optical components, even in the state agnostic setting. Finally, we establish a lower bound on the sample complexity of estimating Wigner negativity, allowing a direct comparison with our protocol. Our results provide both a unifying theoretical framework for non-Gaussianity and a practical route toward its experimental quantification.

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