A New Definition of Quantum Superposition

[2606.15607] A New Definition of Quantum Superposition Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2606.15607 (quant-ph) [Submitted on 14 Jun 2026 ( v1 ), last revised 16 Sep 2026 (this version, v3)] Title: A New Definition of Quantum Superposition Authors: Stephen Bruce Sontz View PDF HTML (experimental) Abstract: The usual description of the superposition of two (pure quantum) states is ambiguous, since the binary operation of addition in a Hilbert space does not pass down to the quotient projective space. In the setting of complex projective space this paper gives a new geometrical definition of the superposition of two pure states, viewed as two distinct points in the projective space, as the unique (complex) line on which those two points lie. Using the Erlangen program the geometry appropriate for quantum theory of the projective space is precisely defined. Also this rigorous approach is compared with others. Comments: 10 pages. Submission for SciPost Subjects: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph) MSC classes: 81P05, 81P16 Cite as: arXiv:2606.15607 [quant-ph] (or arXiv:2606.15607v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.15607 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Stephen Sontz [ view email ] [v1] Sun, 14 Jun 2026 05:28:28 UTC (8 KB) [v2] Tue, 25 Aug 2026 00:05:04 UTC (12 KB) [v3] Wed, 16 Sep 2026 19:18:06 UTC (40 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-06 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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