On some states minimizing uncertainty relations: A new look at these relations

[2411.08131] On some states minimizing uncertainty relations: A new look at these relations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2411.08131 (quant-ph) [Submitted on 12 Nov 2024 ( v1 ), last revised 11 Apr 2026 (this version, v6)] Title: On some states minimizing uncertainty relations: A new look at these relations Authors: Krzysztof Urbanowski View a PDF of the paper titled On some states minimizing uncertainty relations: A new look at these relations, by Krzysztof Urbanowski View PDF HTML (experimental) Abstract: Analyzing Heisenberg--Robertson (HR) and Schrödinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard deviations of a pair of non--commuting observables, $A$ and $B$, is zero, and which differ from those described in the literature. These states are not eigenstates of either the observable $A$ or $B$. The correlation function for these observables in such states is equal to zero. We have also shown that the so--called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states. We additionally show that the uncertainty principle in its most general form has two faces: one is that it is a lower bound on the product of standard deviations, and the other is that the product of standard deviations is an upper bound on the modulus of the correlation function of a pair of the non--commuting observables in the state under consideration. Comments: 17 pages, new comments added, Modern Physics Letters A - accepted Subjects: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph) Cite as: arXiv:2411.08131 [quant-ph] (or arXiv:2411.08131v6 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2411.08131 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Modern Physics Letters A (MPLA), vol. 41, No 21, Article No. 2650106, (2026) Related DOI : https://doi.org/10.1142/S0217732326501063 Focus to learn more DOI(s) linking to related resources Submission history From: Krzysztof Urbanowski [ view email ] [v1] Tue, 12 Nov 2024 19:14:05 UTC (8 KB) [v2] Fri, 27 Dec 2024 19:49:45 UTC (10 KB) [v3] Tue, 11 Feb 2025 09:29:22 UTC (12 KB) [v4] Mon, 17 Mar 2025 11:06:39 UTC (12 KB) [v5] Mon, 14 Jul 2025 16:10:34 UTC (13 KB) [v6] Sat, 11 Apr 2026 12:30:59 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled On some states minimizing uncertainty relations: A new look at these relations, by Krzysztof Urbanowski View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-11 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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