{"paper":{"title":"Limit Theorem for Continuous-Time Quantum Walk on the Line","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Norio Konno","submitted_at":"2004-08-23T06:04:33Z","abstract_excerpt":"Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric distribution on the line, whose evolution is described by the Hadamard transformation, it was proved by the author that the following weak limit theorem holds: X^{(d)}_t /t \\to dx / \\pi (1-x^2) \\sqrt{1 - 2 x^2} as t \\to \\infty. The present paper shows that a similar type of weak limit theorems is satisfied for a {\\it continuous-time} quantum walk X^{(c)}_t on the line as follows: X^{(c)}_t /t \\to dx / \\pi \\sqrt{1 - x^2} as t \\to \\infty. These results for quantum walks form a striking contrast to the central limit theorem for sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0408140","kind":"arxiv","version":5},"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/quant-ph/0408140/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"}