Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers

• URL: http://arxiv.org/abs/2602.18816v1
• Date: Sat, 21 Feb 2026 12:20:23 GMT
• Title: Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers
• Authors: Mrinmoy Samanta, Sudipta Mondal, Ayan Patra, Saptarshi Roy, Aditi Sen De,
• Abstract summary: We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems.<n>For arbitrary pure multimode Gaussian states, we prove that the $2$-local ergotropic gap is a faithful entanglement monotone across any bipartition.<n>We show that the $k$-ergotropic score faithfully quantifies multimode entanglement across $k$ partitions.
• Score: 3.11869200168298
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a thermodynamic characterization of multimode entanglement in pure continuous-variable systems by quantifying the gap between globally and locally extractable work (ergotropy). For arbitrary pure multimode Gaussian states, we prove that the $2$-local ergotropic gap is a faithful entanglement monotone across any bipartition and constitutes a functionally independent upper bound to the Renyi-2 entanglement entropy. We further introduce the $k$-ergotropic score, the minimum $k$-local ergotropic gap, and show that it faithfully quantifies multimode entanglement across $k$ partitions. For pure three-mode Gaussian states, we derive its closed-form relation with the geometric measure for genuine multimode entanglement $(k=2)$, and total Gaussian multimode entanglement $(k=3)$. For systems with more than three modes, the $k$-ergotropic score becomes a functionally independent measure of multimode entanglement to the standard geometric measures. Our results reveal a direct operational hierarchy linking Gaussian multimode entanglement to work extraction under locality constraints, and provide a computable and experimentally accessible thermodynamic framework for characterizing quantum correlations.

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