Generalized Uncertainty Relations and Quantum Speed Limits
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Quantum Physics arXiv:2604.24791 (quant-ph) [Submitted on 25 Apr 2026] Title:Generalized Uncertainty Relations and Quantum Speed Limits Authors:M.W. AlMasri View a PDF of the paper titled Generalized Uncertainty Relations and Quantum Speed Limits, by M.W. AlMasri View PDF HTML (experimental) Abstract:We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid kinetic operator through spectral calculus, we derive exact generalized uncertainty relations that interpolate between $q$-deformed and fractional quantum mechanical bounds. Furthermore, we establish a rigorous quantum speed limit theorem for the hybrid Hamiltonian, revealing how deformation parameters, fractional orders, and external potentials tune the fundamental evolution rate of quantum states. We prove that algebraic deformation accelerates coherent dynamics through discrete momentum quantization, while fractional non-locality induces spectral broadening that suppresses evolution speed. The framework recovers standard quantum mechanics, $q$-quantum mechanics, and fractional quantum mechanics as limiting cases, and provides explicit phenomenological signatures for experimental discrimination in trapped-ion, superconducting, and cold-atom platforms. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.24791 [quant-ph] (or arXiv:2604.24791v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.24791 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mohammad Walid AlMasri [view email] [v1] Sat, 25 Apr 2026 12:22:40 UTC (17 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalized Uncertainty Relations and Quantum Speed Limits, by M.W. AlMasriView 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?)