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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.04932 |
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| _version_ | 1866909677459079168 |
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| author | Gyhm, Ju-Yeon Rosa, Dario Šafránek, Dominik |
| author_facet | Gyhm, Ju-Yeon Rosa, Dario Šafránek, Dominik |
| contents | Understanding the Lie algebraic structure of a physical problem often makes it easier to find its solution. In this paper, we focus on the Lie algebra of Gaussian-conserving superoperators. We construct a Lie algebra of $n$-mode states, $\mathfrak{go}(n)$, composed of all superoperators conserving Gaussianity, and we find it isomorphic to $\mathbb{R}^{2n^2+3n}\oplus_{\mathrm{S}}\mathfrak{gl}(2n,\mathbb{R})$. This allows us to solve the quadratic-order Redfield equation for any, even non-Gaussian, state. We find that the algebraic structure of Gaussian operations is the same as that of super-Poincaré algebra in three-dimensional spacetime, where the CPTP condition corresponds to the combination of causality and directionality of time flow. Additionally, we find that a bosonic density matrix satisfies both the Klein-Gordon and the Dirac equations. Finally, we expand the algebra of Gaussian superoperators even further by relaxing the CPTP condition. We find that it is isomorphic to a superconformal algebra, which represents the maximal symmetry of the field theory. This suggests a deeper connection between two seemingly unrelated fields, with the potential to transform problems from one domain into another where they may be more easily solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Open Quantum Dynamics and Isomorphism to Superconformal Symmetry Gyhm, Ju-Yeon Rosa, Dario Šafránek, Dominik Quantum Physics High Energy Physics - Theory Mathematical Physics Understanding the Lie algebraic structure of a physical problem often makes it easier to find its solution. In this paper, we focus on the Lie algebra of Gaussian-conserving superoperators. We construct a Lie algebra of $n$-mode states, $\mathfrak{go}(n)$, composed of all superoperators conserving Gaussianity, and we find it isomorphic to $\mathbb{R}^{2n^2+3n}\oplus_{\mathrm{S}}\mathfrak{gl}(2n,\mathbb{R})$. This allows us to solve the quadratic-order Redfield equation for any, even non-Gaussian, state. We find that the algebraic structure of Gaussian operations is the same as that of super-Poincaré algebra in three-dimensional spacetime, where the CPTP condition corresponds to the combination of causality and directionality of time flow. Additionally, we find that a bosonic density matrix satisfies both the Klein-Gordon and the Dirac equations. Finally, we expand the algebra of Gaussian superoperators even further by relaxing the CPTP condition. We find that it is isomorphic to a superconformal algebra, which represents the maximal symmetry of the field theory. This suggests a deeper connection between two seemingly unrelated fields, with the potential to transform problems from one domain into another where they may be more easily solved. |
| title | Gaussian Open Quantum Dynamics and Isomorphism to Superconformal Symmetry |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.04932 |