Measuring non-Gaussianity with Correlation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912556274155520 |
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| author | Hahn, Oliver Takagi, Ryuji |
| author_facet | Hahn, Oliver Takagi, Ryuji |
| contents | 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 Rényi-$α$ entropy for pure states and Rényi-$α$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring non-Gaussianity with Correlation Hahn, Oliver Takagi, Ryuji Quantum Physics 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 Rényi-$α$ entropy for pure states and Rényi-$α$ 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. |
| title | Measuring non-Gaussianity with Correlation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.19890 |