Quantum Fidelity on Krein and S-spaces
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Quantum Physics arXiv:2606.09939 (quant-ph) [Submitted on 7 Jun 2026] Title:Quantum Fidelity on Krein and S-spaces Authors:Morgan Jones View a PDF of the paper titled Quantum Fidelity on Krein and S-spaces, by Morgan Jones View PDF HTML (experimental) Abstract:The notion of Fidelity for quantum states is a measure of how much two states overlap. In the matrix formalism of quantum mechanics, states are represented by density operators i.e. positive semi-definite matrices with trace equal to 1 in a complex Euclidean space $M_n(\mathbb{C})$. The notion of quantum states in this setting has already started to be considered. We will define an analogous notion of measurement for so-called $J$-states and use it to show that a notion of fidelity holds in the Krein setting. We will also show that there exists an analogous result to the Fuchs-Caves measurement holds in the Krein setting. We will then will extend this definition of fidelity to so-called $U$-quantum states on $S$-spaces. We will demonstrate that the analogous geometric motivation holds in the Krein and $S$-space setting, as holds for quantum fidelity and geometric means of operators. Subjects: Quantum Physics (quant-ph); Functional Analysis (math.FA) Cite as: arXiv:2606.09939 [quant-ph] (or arXiv:2606.09939v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.09939 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Morgan Jones [view email] [v1] Sun, 7 Jun 2026 22:11:49 UTC (17 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Fidelity on Krein and S-spaces, by Morgan JonesView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: math math.FA 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?)