Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers
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| Format: | Preprint |
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2026
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| _version_ | 1866915811015262208 |
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| author | Samanta, Mrinmoy Mondal, Sudipta Patra, Ayan Roy, Saptarshi De, Aditi Sen |
| author_facet | Samanta, Mrinmoy Mondal, Sudipta Patra, Ayan Roy, Saptarshi De, Aditi Sen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_18816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers Samanta, Mrinmoy Mondal, Sudipta Patra, Ayan Roy, Saptarshi De, Aditi Sen Quantum Physics 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. |
| title | Hierarchies of Gaussian multimode entanglement from thermodynamic quantifiers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.18816 |