Gaussian dynamics in the double Siegel disk
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910045837459456 |
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| author | Pantaleoni, Giacomo Menicucci, Nicolas C. |
| author_facet | Pantaleoni, Giacomo Menicucci, Nicolas C. |
| contents | We show that deterministic multimode Gaussian channels admit a symmetric-space description. Passing from the n-mode Siegel disk to a doubled version of that space lets general Gaussian dynamics act by a linear-fractional (Mobius) transformation on a single matrix parameter. This doubled disk naturally parametrizes Gaussian kernels in the Fock-Bargmann representation, and contains an explicit physical subset corresponding to valid mixed Gaussian states. Starting from the standard X,Y parametrization of a deterministic Gaussian channel, we construct a normalized oscillator-semigroup element whose fractional action reproduces the channel update on that subset; Gaussian unitaries appear as the symplectic, isometric special case. This gives a bridge between covariance-matrix channel theory and the adjacency-matrix or symmetric-space picture, preserves a simple composition law given by matrix multiplication of the acting blocks, and suggests a direct route to graphical update rules beyond pure states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05824 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian dynamics in the double Siegel disk Pantaleoni, Giacomo Menicucci, Nicolas C. Quantum Physics We show that deterministic multimode Gaussian channels admit a symmetric-space description. Passing from the n-mode Siegel disk to a doubled version of that space lets general Gaussian dynamics act by a linear-fractional (Mobius) transformation on a single matrix parameter. This doubled disk naturally parametrizes Gaussian kernels in the Fock-Bargmann representation, and contains an explicit physical subset corresponding to valid mixed Gaussian states. Starting from the standard X,Y parametrization of a deterministic Gaussian channel, we construct a normalized oscillator-semigroup element whose fractional action reproduces the channel update on that subset; Gaussian unitaries appear as the symplectic, isometric special case. This gives a bridge between covariance-matrix channel theory and the adjacency-matrix or symmetric-space picture, preserves a simple composition law given by matrix multiplication of the acting blocks, and suggests a direct route to graphical update rules beyond pure states. |
| title | Gaussian dynamics in the double Siegel disk |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.05824 |