A universal complementarity identity for polarized double-slit interferometry
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Quantum Physics arXiv:2604.18760 (quant-ph) [Submitted on 20 Apr 2026] Title:A universal complementarity identity for polarized double-slit interferometry Authors:José J. Gil View a PDF of the paper titled A universal complementarity identity for polarized double-slit interferometry, by Jos\'e J. Gil View PDF HTML (experimental) Abstract:We establish an exact identity among four dimensionless invariants accessible by standard polarimetric and interferometric measurements in a polarized double-slit experiment: the in-phase and quadrature components V_A and V_N of fringe visibility, the path predictability P, and the mixedness I of the path-reduced state satisfy V_A^2 + V_N^2 + P^2 + I^2 = 1. The identity is a universal algebraic consequence of the positivity of the reduced state and holds for every normalized path-polarization density matrix. It unifies the Englert-Greenberger-Yasin and Jakob-Bergou relations, separates the two operationally distinct components of visibility measurable by phase-shifted interferometry, and admits a natural interpretation within the Jaynes maximum-entropy framework: the three path invariants parametrize the minimal exponential family on the accessible algebra, while I^2 emerges as the residual mixedness that saturates the positivity bound. The separation V^2 = V_A^2 + V_N^2 identifies the antisymmetric sector of the coherence matrix rho = A + iN as the specific substrate of phase-sensitive information and permits a sector-resolved diagnosis of environmental coupling. Comments: Subjects: Quantum Physics (quant-ph); Optics (physics.optics) Cite as: arXiv:2604.18760 [quant-ph] (or arXiv:2604.18760v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.18760 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jose Jorge Gil [view email] [v1] Mon, 20 Apr 2026 19:09:51 UTC (401 KB) Full-text links: Access Paper: View a PDF of the paper titled A universal complementarity identity for polarized double-slit interferometry, by Jos\'e J. GilView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: physics physics.optics 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?)