Spectral-angular parametrization of open qudit dynamics
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Quantum Physics arXiv:2604.11864 (quant-ph) [Submitted on 13 Apr 2026] Title:Spectral-angular parametrization of open qudit dynamics Authors:Jean-Pierre Gazeau, Kaoutar El Bachiri, Zakaria Bouameur, Yassine Hassouni View a PDF of the paper titled Spectral-angular parametrization of open qudit dynamics, by Jean-Pierre Gazeau and 3 other authors View PDF HTML (experimental) Abstract:We present a parametrization of density matrices (mixed states) in a finite-dimensional Hilbert space $\mathbb{C}^n$, particularly suited to the description of their time evolution as open quantum systems governed by GKLS dynamics. A generic (non-degenerate) density matrix $rho_{\mathbf{r},\pmb{\phi}}$, characterized by $n^2-1$ real parameters, naturally decomposes into two sets: (i) an $(n-1)$-tuple $\mathbf{r}$ of spectral parameters, constrained to lie in a convex polytope, and (ii) a set of $n^2-n$ angular variables $\pmb{\phi}$, associated with the flag manifold $\simeq \mathrm{SU}(n)/\mathbb{T}^{n-1}$, where $\mathbb{T}^{n-1}$ is the standard maximal diagonal torus, in the spirit of the Tilma--Sudarshan construction. A key observation is that the spectral parameters $\mathbf{r} = (r_1, \ldots, r_{n-1})$ admit a natural Lie-algebraic interpretation: they are precisely the simple root coordinates of the eigenvalue vector in the Cartan subalgebra of $A_{n-1} = \mathfrak{sl}(n)$, with each $r_i = p_i - p_{i+1}$ corresponding to the simple root $\alpha_i = e_i - e_{i+1}$. The convex polytope constraining $\mathbf{r}$ is thus the positive Weyl chamber of $A_{n-1}$, and the full spectral domain $R_{n-1}$ is the corresponding weight polytope. This parametrization leads to a partial decoupling of the dynamics: the evolution of the angular variables depends on both the Hamiltonian and the dissipative part of the Lindblad generator, whereas the evolution of the spectral parameters involves only the dissipative contribution. Low-dimensional examples for $n=2$ and $n=3$ are discussed in detail, including an application to the trichromatic structure of human colour perception, and we propose an alternative definition of purity expressed solely in terms of the spectral parameters $\mathbf{r}$. Comments: Subjects: Quantum Physics (quant-ph) MSC classes: 81P16, 81R05, 81R30, 81S22 Cite as: arXiv:2604.11864 [quant-ph] (or arXiv:2604.11864v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.11864 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jean Pierre Gazeau [view email] [v1] Mon, 13 Apr 2026 16:02:24 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral-angular parametrization of open qudit dynamics, by Jean-Pierre Gazeau and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)