Related papers: Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems

Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems

URL: http://arxiv.org/abs/2512.18410v1
Date: Sat, 20 Dec 2025 16:18:55 GMT
Title: Partner-mode overlap as a symplectic-invariant measure of correlations in Gaussian Systems
Authors: Ivan Agullo, Eduardo Martín-Martínez, Sergi Nadal-Gisbert, Koji Yamaguchi,
Abstract summary: We introduce a locally symplectic-invariant quantifier of correlations between two different arbitrary modes in bosonic Gaussian systems.<n>This quantity admits a simple interpretation as an overlap between each mode and the purification partner of the other.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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