{"paper":{"title":"Quasilinear evolution versus von Neumann selective measurement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A nonlinear generalization of the von Neumann equation replaces instantaneous projection with continuous quasilinear evolution in selective quantum measurements.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jakub Rembieli\\'nski, Karol {\\L}awniczak","submitted_at":"2026-05-13T16:36:41Z","abstract_excerpt":"In this article, we introduce a new form of quantum selective measurement in which the von Neumann projection postulate is replaced by quasilinear evolution, governed by a nonlinear generalization of the von Neumann equation. We demonstrate that this equation preserves the equivalence of quantum ensembles and, consequently, satisfies the no-signalling principle, ensuring consistency with both quantum mechanics and Einstein causality. Our approach eliminates the need for instantaneous, discontinuous state collapse and provides a unified description of the postmeasurement quantum state reduction"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a new form of quantum selective measurement in which the von Neumann projection postulate is replaced by quasilinear evolution, governed by a nonlinear generalization of the von Neumann equation... it preserves the equivalence of quantum ensembles and, consequently, satisfies the no-signalling principle.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The specific nonlinear generalization of the von Neumann equation is assumed to preserve ensemble equivalence and no-signaling without additional constraints or post-selection, as stated in the abstract without derivation details.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quasilinear evolution replaces von Neumann projection for selective measurements, providing continuous state reduction without collapse while satisfying no-signaling and Born rule.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A nonlinear generalization of the von Neumann equation replaces instantaneous projection with continuous quasilinear evolution in selective quantum measurements.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"343ec7497ee3babc96d88c356dee593830626a7620a77427c632fed96ea94d40"},"source":{"id":"2605.13756","kind":"arxiv","version":1},"verdict":{"id":"5e352c0b-af81-40c3-92ae-7d9d7bb8578e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:52:40.030460Z","strongest_claim":"We introduce a new form of quantum selective measurement in which the von Neumann projection postulate is replaced by quasilinear evolution, governed by a nonlinear generalization of the von Neumann equation... it preserves the equivalence of quantum ensembles and, consequently, satisfies the no-signalling principle.","one_line_summary":"Quasilinear evolution replaces von Neumann projection for selective measurements, providing continuous state reduction without collapse while satisfying no-signaling and Born rule.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The specific nonlinear generalization of the von Neumann equation is assumed to preserve ensemble equivalence and no-signaling without additional constraints or post-selection, as stated in the abstract without derivation details.","pith_extraction_headline":"A nonlinear generalization of the von Neumann equation replaces instantaneous projection with continuous quasilinear evolution in selective quantum measurements."},"references":{"count":55,"sample":[{"doi":"","year":2026,"title":"Quasilinear evolution versus von Neumann selective measurement","work_id":"1005e578-e4fd-46b5-ac7b-27c7a3796296","ref_index":1,"cited_arxiv_id":"2605.13756","is_internal_anchor":true},{"doi":"","year":null,"title":"The following figure presents the state dy- namics under the scaleg0 much lower and much higher than in previous examples","work_id":"bf7c1f56-e269-4e74-bc5c-4c744fa6f9e9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Figure 7 presents the state dynamics for two orientations ofg","work_id":"97e91ed6-ff34-4078-905d-30dcc190df5e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"In the case of the inverted Morse potential, the shape parameterκmay be adjusted","work_id":"1f19d07f-5bac-459e-9660-8d45c3047579","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"J. 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