{"paper":{"title":"A universal complementarity identity for polarized double-slit interferometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Four measurable quantities in polarized double-slit experiments satisfy the exact identity V_A squared plus V_N squared plus P squared plus I squared equals one.","cross_cats":["physics.optics"],"primary_cat":"quant-ph","authors_text":"Jos\\'e J. Gil","submitted_at":"2026-04-20T19:09:51Z","abstract_excerpt":"An exact identity is established among four experimentally accessible quantities in polarized double-slit interferometry: the phase-reference-dependent in-phase and quadrature components $V_A$ and $V_N$ of fringe visibility, the path predictability $\\mathcal{P}$, and the mixedness $\\mathcal{I}$ of the reduced path state satisfy $V_A^2+V_N^2+\\mathcal{P}^2+\\mathcal{I}^2=1$. The identity is an algebraic consequence of positivity and holds for every normalized path--polarization density matrix. It contains the Greenberger--Yasin predictability bound and, for globally pure path--polarization states"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish an exact identity among four dimensionless invariants ... 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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduced path-polarization density matrix is positive semidefinite (a standard quantum-mechanical requirement) and normalized; if this fails for the physical system under study the identity would not hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In polarized double-slit interferometry the sum of the squares of in-phase visibility, quadrature visibility, path predictability, and path-state mixedness equals one for any normalized density matrix.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Four measurable quantities in polarized double-slit experiments satisfy the exact identity V_A squared plus V_N squared plus P squared plus I squared equals one.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a3297185e560bfe68c58c00095a276b325dd7464d144e9ccaf69533193ec0d22"},"source":{"id":"2604.18760","kind":"arxiv","version":2},"verdict":{"id":"f7280895-8aa9-4091-994c-1318581e236e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T04:16:22.931146Z","strongest_claim":"We establish an exact identity among four dimensionless invariants ... 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.","one_line_summary":"In polarized double-slit interferometry the sum of the squares of in-phase visibility, quadrature visibility, path predictability, and path-state mixedness equals one for any normalized density matrix.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduced path-polarization density matrix is positive semidefinite (a standard quantum-mechanical requirement) and normalized; if this fails for the physical system under study the identity would not hold.","pith_extraction_headline":"Four measurable quantities in polarized double-slit experiments satisfy the exact identity V_A squared plus V_N squared plus P squared plus I squared equals one."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.18760/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-20T03:43:02.570155Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"13041389b194f6fe17074363958580b60ce16392120fa7a3140839e2559c24f6"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}