Contractivity of the Hilbert--Schmidt Speed in Unital Quantum Channels: Foundation for Witnessing Non-Markovianity and Discriminating Unital from Non-Unital Markovian Dynamics

Quantum Physics arXiv:2607.05619 (quant-ph) [Submitted on 6 Jul 2026] Title:Contractivity of the Hilbert--Schmidt Speed in Unital Quantum Channels: Foundation for Witnessing Non-Markovianity and Discriminating Unital from Non-Unital Markovian Dynamics Authors:Hossein Rangani Jahromi View a PDF of the paper titled Contractivity of the Hilbert--Schmidt Speed in Unital Quantum Channels: Foundation for Witnessing Non-Markovianity and Discriminating Unital from Non-Unital Markovian Dynamics, by Hossein Rangani Jahromi View PDF HTML (experimental) Abstract:We investigate the Hilbert--Schmidt speed (HSS), a geometric indicator defined through the Hilbert--Schmidt norm of the tangent vector to a parametrized family of quantum states, under general open-system dynamics. Working in the framework of finite-dimensional, parameter-independent completely positive trace-preserving (CPTP) evolution where the parameter is encoded solely in the initial state, we prove that the HSS is contractive under every unital CPTP map. Consequently, for any CP-divisible evolution whose intermediate propagators are unital, the HSS is monotonically non-increasing in time. We then establish the generator-level counterpart for Markovian dynamics governed by a Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) master equation with Hermitian Lindblad operators, deriving an explicit non-positive expression for the time derivative of the squared HSS. These results provide a rigorous foundation for using HSS backflow as a sufficient witness of non-Markovianity in physical settings where the relevant CP-divisible Markovian dynamics is known \emph{a priori} to be unital. Conversely, we show by an explicit qutrit counterexample that HSS can increase even in perfectly Markovian but non-unital dynamics, demonstrating that HSS non-monotonicity is not, in general, a faithful indicator of memory effects unless unitality is guaranteed. Our findings clarify the exact scope of HSS-based diagnostics and identify unitality as the crucial structural ingredient underlying their validity. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.05619 [quant-ph] (or arXiv:2607.05619v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.05619 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hossein Rangani Jahromi [view email] [v1] Mon, 6 Jul 2026 20:29:59 UTC (10 KB) Full-text links: Access Paper: View a PDF of the paper titled Contractivity of the Hilbert--Schmidt Speed in Unital Quantum Channels: Foundation for Witnessing Non-Markovianity and Discriminating Unital from Non-Unital Markovian Dynamics, by Hossein Rangani JahromiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)