Gaussian dynamics in the double Siegel disk
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Quantum Physics arXiv:2603.05824 (quant-ph) [Submitted on 6 Mar 2026] Title:Gaussian dynamics in the double Siegel disk Authors:Giacomo Pantaleoni, Nicolas C. Menicucci View a PDF of the paper titled Gaussian dynamics in the double Siegel disk, by Giacomo Pantaleoni and 1 other authors View PDF Abstract:We show that multimode deterministic (CPTP) Gaussian channels admit a symmetric-space description: by passing from the \(n\)-mode Siegel disk \(\Delta_{n}\) to the \(2n\)-mode \emph{double Siegel disk} \(\Delta_{2n}\), general Gaussian dynamics becomes a linear-fractional (Möbius) action on a single matrix representative. Concretely, \(\Delta_{2n}\) naturally parametrizes Gaussian kernels in the Fock--Bargmann representation, and we identify an explicit physical subset \(\sspace\subset\Delta_{2n}\) corresponding to valid mixed Gaussian states. We then construct, from the standard \((X,Y)\) parametrization of a deterministic Gaussian channel, a normalized oscillator-semigroup element \(\bar E\) whose fractional action implements the channel update \(\amat\mapsto\phi_{\bar E}(\amat)\) on \(\sspace\); Gaussian unitaries arise as the symplectic (isometric) subcase. The resulting calculus bridges covariance-matrix channel theory with the adjacency-matrix/symmetric-space picture, retains a simple composition law (matrix multiplication of the acting blocks), and suggests a direct route to graphical update rules beyond the pure-state setting. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.05824 [quant-ph] (or arXiv:2603.05824v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.05824 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Giacomo Pantaleoni [view email] [v1] Fri, 6 Mar 2026 02:19:04 UTC (51 KB) Full-text links: Access Paper: View a PDF of the paper titled Gaussian dynamics in the double Siegel disk, by Giacomo Pantaleoni and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)