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A universal complementarity identity for polarized double-slit interferometry

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arXiv:2604.18760v1 Announce Type: new 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

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Quantum Physics [Submitted on 20 Apr 2026] A universal complementarity identity for polarized double-slit interferometry José J. Gil 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: 11 pages, 1 figure 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 Submission history From: Jose Jorge Gil [view email] [v1] Mon, 20 Apr 2026 19:09:51 UTC (401 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: physics physics.optics References & Citations INSPIRE HEP NASA ADS 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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