{"paper":{"title":"Quantum Zeno-like Paradox for Position Measurements: A Particle Precisely Found in Space is Nowhere to be Found in Hilbert Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Roderich Tumulka, Xabier Oianguren-Asua","submitted_at":"2026-01-27T10:50:49Z","abstract_excerpt":"On a quantum particle in the unit interval $[0,1]$, perform a position measurement with inaccuracy $1/n$ and then a quantum measurement of the projection $|\\phi\\rangle\\langle\\phi|$ with some arbitrary but fixed normalized $\\phi$. Call the outcomes $X \\in[0,1]$ and $Y \\in\\{0,1\\}$. We show that in the limit $n\\to\\infty$ corresponding to perfect precision for $X$, the probability of $Y=1$ tends to 0 for every $\\phi$. Since there is no density matrix, pure or mixed, which upon measurement of any $|\\phi\\rangle\\langle\\phi|$ yields outcome 1 with probability 0, our result suggests that a novel type o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.19469","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.19469/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}