Representation theory of inhomogeneous Gaussian unitaries

• URL: http://arxiv.org/abs/2602.08611v1
• Date: Mon, 09 Feb 2026 12:55:28 GMT
• Title: Representation theory of inhomogeneous Gaussian unitaries
• Authors: Jingqi Sun, Joshua Combes, Lucas Hackl,
• Abstract summary: We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by $(M,z,)$.<n>We derive the group multiplication law from the Baker-Campbel-Hausdorff formula.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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