Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911329228423168 |
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| author | Agullo, Ivan Martín-Martínez, Eduardo Nadal-Gisbert, Sergi Yamaguchi, Koji |
| author_facet | Agullo, Ivan Martín-Martínez, Eduardo Nadal-Gisbert, Sergi Yamaguchi, Koji |
| contents | We introduce a locally symplectic-invariant quantifier of correlations between two different arbitrary modes in bosonic Gaussian systems, denoted by $\mathcal{D}^{\mathrm{sym}}$. This quantity admits a simple geometric interpretation as an overlap between each mode and the purification partner of the other, formulated using the complex-structure description of Gaussian states. The construction builds on the partner-mode framework of Ref.~\cite{agullo_correlation_2025} and can be viewed as a symmetrized extension of earlier overlap-based measures~\cite{osawa2025entanglement}. We formulate a simple necessary and sufficient criterion for two-mode entanglement in Gaussian states in terms of $\mathcal{D}^{\mathrm{sym}}$, placing on firm quantitative footing the intuition that entanglement with a given localized mode `lives' on the spatial support of its partner mode. We illustrate the framework with a numerical analysis of a scalar field in Minkowski spacetime and discuss its extension to multimode systems and mixed Gaussian states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems Agullo, Ivan Martín-Martínez, Eduardo Nadal-Gisbert, Sergi Yamaguchi, Koji Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory We introduce a locally symplectic-invariant quantifier of correlations between two different arbitrary modes in bosonic Gaussian systems, denoted by $\mathcal{D}^{\mathrm{sym}}$. This quantity admits a simple geometric interpretation as an overlap between each mode and the purification partner of the other, formulated using the complex-structure description of Gaussian states. The construction builds on the partner-mode framework of Ref.~\cite{agullo_correlation_2025} and can be viewed as a symmetrized extension of earlier overlap-based measures~\cite{osawa2025entanglement}. We formulate a simple necessary and sufficient criterion for two-mode entanglement in Gaussian states in terms of $\mathcal{D}^{\mathrm{sym}}$, placing on firm quantitative footing the intuition that entanglement with a given localized mode `lives' on the spatial support of its partner mode. We illustrate the framework with a numerical analysis of a scalar field in Minkowski spacetime and discuss its extension to multimode systems and mixed Gaussian states. |
| title | Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.18410 |