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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2602.08611 |
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| _version_ | 1866911434519085056 |
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| author | Sun, Jingqi Combes, Joshua Hackl, Lucas |
| author_facet | Sun, Jingqi Combes, Joshua Hackl, Lucas |
| contents | Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,Ψ)$. The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representation theory of inhomogeneous Gaussian unitaries Sun, Jingqi Combes, Joshua Hackl, Lucas Quantum Physics Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,Ψ)$. The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law. |
| title | Representation theory of inhomogeneous Gaussian unitaries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.08611 |